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Volumn , Issue , 2007, Pages 1-361

An introduction to Gödel’s theorems

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EID: 84924003054     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1017/CBO9780511800962     Document Type: Book
Times cited : (118)

References (223)
  • 1
    • 85066357221 scopus 로고
    • On Hilbert’s construction of the real numbers, van Heijenoort 1967
    • Ackermann, W., 1928. On Hilbert’s construction of the real numbers. In van Heijenoort 1967, pp. 495-507.
    • (1928) , pp. 495-507
    • Ackermann, W.1
  • 3
    • 37049022078 scopus 로고    scopus 로고
    • Number theory and elementary arithmetic
    • Avigad, J., 2003. Number theory and elementary arithmetic. Philosophia Mathematica, 11: 257-284.
    • (2003) Philosophia Mathematica , vol.11 , pp. 257-284
    • Avigad, J.1
  • 5
    • 0031495154 scopus 로고    scopus 로고
    • The impact of the lambda calculus in logic and computer science
    • Barendregt, H., 1997. The impact of the Lambda Calculus in logic and computer science. Bulletin of Symbolic Logic, 3: 181-215.
    • (1997) Bulletin of Symbolic Logic , vol.3 , pp. 181-215
    • Barendregt, H.1
  • 6
    • 0010167339 scopus 로고
    • God, the devil and gödel
    • Benacerraf, P., 1967. God, the Devil and Gödel. The Monist,51: 9-32.
    • (1967) The Monist , vol.51 , pp. 9-32
    • Benacerraf, P.1
  • 7
    • 85066386235 scopus 로고
    • The philosophy of mathematics and Hilbertian proof-theory, Mancosu 1998
    • Bernays, P., 1930. The philosophy of mathematics and Hilbertian proof-theory. In Mancosu 1998, pp. 234-265.
    • (1930) , pp. 234-265
    • Bernays, P.1
  • 9
    • 50249181333 scopus 로고    scopus 로고
    • Proving church’s thesis
    • Black, R., 2000. Proving Church’s Thesis. Philosophia Mathematica,8: 244-258.
    • (2000) Philosophia Mathematica , vol.8 , pp. 244-258
    • Black, R.1
  • 10
    • 85066360372 scopus 로고    scopus 로고
    • Algorithms: a quest for absolute definitions, Olszewski et al. (2006
    • Blass, A. and Gurevich, Y., 2006. Algorithms: a quest for absolute definitions. In Olszewski et al. (2006), pp. 24-57.
    • (2006) , pp. 24-57
    • Blass, A.1    Gurevich, Y.2
  • 12
    • 0003982491 scopus 로고    scopus 로고
    • Cambridge, MA: Harvard University Press
    • Boolos, G., 1998. Logic, Logic, and Logic.Cambridge, MA: Harvard University Press.
    • (1998) Logic, Logic, and Logic
    • Boolos, G.1
  • 15
    • 0009627186 scopus 로고
    • Oxford Logic Guides, Oxford: Clarendon Press
    • Bridge, J., 1977. Beginning Model Theory.Oxford Logic Guides 1. Oxford: Clarendon Press.
    • (1977) Beginning Model Theory , vol.1
    • Bridge, J.1
  • 18
    • 21844505230 scopus 로고
    • On gödel’s theorems on lengths of proofs i: Number of lines and speedups for arithmetic
    • Buss, S. R., 1994. On Gödel’s theorems on lengths of proofs I: number of lines and speedups for arithmetic. Journal of Symbolic Logic, 39: 737-756.
    • (1994) Journal of Symbolic Logic , vol.39 , pp. 737-756
    • Buss, S.R.1
  • 19
    • 0012944516 scopus 로고    scopus 로고
    • Proof theory of arithmetic
    • S. R. Buss, Amsterdam: Elsevier Science B.V
    • Buss, S. R., 1998. Proof theory of arithmetic. In S. R. Buss (ed.), Handbook of Proof Theory, pp. 79-147. Amsterdam: Elsevier Science B.V.
    • (1998) Handbook of Proof Theory , pp. 79-147
    • Buss, S.R.1
  • 21
    • 84865576517 scopus 로고
    • On a property of the set of real algebraic numbers, Ewald 1996
    • Cantor, G., 1874. On a property of the set of real algebraic numbers. In Ewald 1996, Vol. 2, pp. 839-843.
    • (1874) , vol.2 , pp. 839-843
    • Cantor, G.1
  • 22
    • 78649707366 scopus 로고
    • On an elementary question in the theory of manifolds, Ewald 1996
    • Cantor, G., 1891. On an elementary question in the theory of manifolds. In Ewald 1996, Vol. 2, pp. 920-922.
    • (1891) , vol.2 , pp. 920-922
    • Cantor, G.1
  • 23
    • 0039560285 scopus 로고
    • Vienna: Springer. Translated into English as Carnap 1937
    • Carnap, R., 1934. Logische Syntax der Sprache.Vienna: Springer. Translated into English as Carnap 1937.
    • (1934) Logische Syntax Der Sprache
    • Carnap, R.1
  • 29
    • 0000954072 scopus 로고
    • An unsolvable problem of elementary number theory
    • Church, A., 1936b. An unsolvable problem of elementary number theory. American Journal of Mathematics,58: 345-363.
    • (1936) American Journal of Mathematics , vol.58 , pp. 345-363
    • Church, A.1
  • 32
    • 4544345817 scopus 로고    scopus 로고
    • Boca Raton, Florida: Chapman and Hall/CRC
    • Cooper, S. B., 2004. Computability Theory.Boca Raton, Florida: Chapman and Hall/CRC.
    • (2004) Computability Theory
    • Cooper, S.B.1
  • 34
    • 0001828076 scopus 로고
    • On axiomatizability within a system
    • Craig, W., 1953. On axiomatizability within a system. Journal of Symbolic Logic,18: 30-32.
    • (1953) Journal of Symbolic Logic , vol.18 , pp. 30-32
    • Craig, W.1
  • 35
    • 0002214625 scopus 로고
    • The inconsistency of certain formal logics
    • Curry, H. B., 1942. The inconsistency of certain formal logics. Journal of Symbolic Logic, 7: 115-117.
    • (1942) Journal of Symbolic Logic , vol.7 , pp. 115-117
    • Curry, H.B.1
  • 36
    • 0003408347 scopus 로고
    • Cambridge: Cambridge University Press
    • Cutland, N. J., 1980. Computability.Cambridge: Cambridge University Press.
    • (1980) Computability
    • Cutland, N.J.1
  • 37
    • 49049136430 scopus 로고
    • Why gödel didn’t have church’s thesis
    • Davis, M., 1982. Why Gödel didn’t have Church’s Thesis. Information and, Control, 54: 3-24.
    • (1982) Information And, Control , vol.54 , pp. 3-24
    • Davis, M.1
  • 38
    • 0004302673 scopus 로고
    • Was sind und was sollen die Zahlen?, Ewald 1996
    • Dedekind, R., 1888. Was sind und was sollen die Zahlen? In Ewald 1996, Vol. 2, pp. 790-833.
    • (1888) , vol.2 , pp. 790-833
    • Dedekind, R.1
  • 42
    • 85066387129 scopus 로고    scopus 로고
    • Epstein, R. L. and Carnielli, W. A., 2000. Computability: Computable Functions, Logic, and the Foundations of Mathematics. Wadsworth.
    • Epstein, R.L.1    Carnielli, W.A.2
  • 44
    • 33745286388 scopus 로고    scopus 로고
    • Hierarchies of provably recursive functions
    • S. R. Buss, Amsterdam: Elsevier Science B.V
    • Fairtlough, M. and Wainer, S. S., 1998. Hierarchies of provably recursive functions. In S. R. Buss (ed.), Handbook of Proof Theory, pp. 149-207. Amsterdam: Elsevier Science B.V.
    • (1998) Handbook of Proof Theory , pp. 149-207
    • Fairtlough, M.1    Wainer, S.S.2
  • 45
    • 0002092865 scopus 로고
    • Arithmetization of metamathematics in a general setting
    • Feferman, S., 1960. Arithmetization of metamathematics in a general setting. Fundamenta Mathematicae,49: 35-92.
    • (1960) Fundamenta Mathematicae , vol.49 , pp. 35-92
    • Feferman, S.1
  • 46
    • 0012220097 scopus 로고
    • Kurt gödel: Conviction and caution
    • Feferman 1998
    • Feferman, S., 1984. Kurt Gödel: conviction and caution. Philosophia Naturalis,21: 546-562. In Feferman 1998, pp. 150-164.
    • (1984) Philosophia Naturalis , vol.21 , pp. 150-164
    • Feferman, S.1
  • 48
    • 0037961232 scopus 로고    scopus 로고
    • Why the programs for new axioms need to be questioned
    • Feferman, S., 2000. Why the programs for new axioms need to be questioned. Bulletin of Symbolic Logic,6: 401-413.
    • (2000) Bulletin of Symbolic Logic , vol.6 , pp. 401-413
    • Feferman, S.1
  • 49
    • 33745610696 scopus 로고    scopus 로고
    • Are there absolutely unsolvable problems? Gödel’s dichotomy
    • Feferman, S., 2006. Are there absolutely unsolvable problems? Gödel’s dichotomy. Philosophia Mathematica,14: 134-152.
    • (2006) Philosophia Mathematica , vol.14 , pp. 134-152
    • Feferman, S.1
  • 53
    • 0013060508 scopus 로고    scopus 로고
    • Church’s thesis: Prelude to a proof
    • Folina, J., 1998. Church’s Thesis: prelude to a proof. Philosophia Mathematica,6: 302-323.
    • (1998) Philosophia Mathematica , vol.6 , pp. 302-323
    • Folina, J.1
  • 54
    • 4544386568 scopus 로고    scopus 로고
    • Association for Symbolic Logic: Lecture Notes in Logic, Wellesley, MA: A. K. Péters
    • Franzén, T., 2004. Inexhaustibility: a Non-Exhaustive Treatment.Association for Symbolic Logic: Lecture Notes in Logic 16. Wellesley, MA: A. K. Péters.
    • (2004) Inexhaustibility: A Non-Exhaustive Treatment , pp. 16
    • Franzén, T.1
  • 56
    • 85066371870 scopus 로고
    • On the scientific justification of a conceptual notation, Frege 1972
    • Frege, G., 1882. On the scientific justification of a conceptual notation. In Frege 1972, pp. 83-89.
    • (1882) , pp. 83-89
    • Frege, G.1
  • 57
    • 0004057759 scopus 로고
    • Verlag von Wilhelm Koebner. Translated as Frege 1950
    • Frege, G., 1884. Die Grundlagen der Arithmetik Breslau: Verlag von Wilhelm Koebner. Translated as Frege 1950.
    • (1884) Die Grundlagen Der Arithmetik
    • Frege, G.1
  • 58
    • 85066386555 scopus 로고
    • Function and concept, Frege 1984
    • Frege, G., 1891. Function and concept. In Frege 1984, pp. 137-156.
    • (1891) , pp. 137-156
    • Frege, G.1
  • 59
    • 85066379653 scopus 로고    scopus 로고
    • Frege, G., 1950. The Foundations of Arithmetic. Basil Blackwell.
    • Frege, G.1
  • 60
    • 0039349530 scopus 로고
    • Berkeley and Los Angeles: University of California Press
    • Frege, G., 1964. The Basic Laws of Arithmetic.Berkeley and Los Angeles: University of California Press.
    • (1964) The Basic Laws of Arithmetic
    • Frege, G.1
  • 63
    • 33645571666 scopus 로고    scopus 로고
    • Normal mathematics will need new axioms
    • Friedman, H., 2000. Normal mathematics will need new axioms. Bulletin of Symbolic Logic, 6: 434-336.
    • (2000) Bulletin of Symbolic Logic , vol.6 , pp. 336-434
    • Friedman, H.1
  • 64
    • 0010201664 scopus 로고
    • What’s so special about kruskal’s theorem and the ordinal to? A survey of some results in proof theory
    • Gallier, J. H., 1991. What’s so special about Kruskal’s theorem and the ordinal To? A survey of some results in proof theory. Annals of Pure and Applied Logic, 53: 199-260.
    • (1991) Annals of Pure and Applied Logic , vol.53 , pp. 199-260
    • Gallier, J.H.1
  • 65
    • 0003150965 scopus 로고
    • The confluence of ideas in 1936
    • R. Herken, Oxford University Press
    • Gandy, R., 1988. The confluence of ideas in 1936. In R. Herken (ed.), The Universal Turing Machine, pp. 55-111. Oxford University Press.
    • (1988) The Universal Turing Machine , pp. 55-111
    • Gandy, R.1
  • 66
    • 27944496797 scopus 로고
    • Untersuchungen uber das logische schliessen
    • Szabo 1969
    • Gentzen, G., 1935. Untersuchungen uber das logische Schliessen. Mathematische Zeitschrift,39: 176-210, 405-431. Translated as ‘Investigations into logical deduction’ in Szabo 1969.
    • (1935) Mathematische Zeitschrift , vol.39
    • Gentzen, G.1
  • 67
    • 0011315928 scopus 로고
    • Die widerspruchsfreiheit der reinen zahlentheorie
    • Szabo 1969
    • Gentzen, G., 1936. Die Widerspruchsfreiheit der reinen Zahlentheorie. Mathematische Annalen,112: 493-565. Translated as ‘The consistency of elementary number theory’ in Szabo 1969.
    • (1936) Mathematische Annalen , vol.112 , pp. 493-565
    • Gentzen, G.1
  • 68
    • 85066365197 scopus 로고
    • Der Unendlichkeitsbegriff in der Mathematik. Unpublished lecture, translated as ‘The concept of infinite in mathematics’ in Szabo 1969
    • Gentzen, G., 1937. Der Unendlichkeitsbegriff in der Mathematik. Unpublished lecture, translated as ‘The concept of infinite in mathematics’ in Szabo 1969.
    • (1937)
    • Gentzen, G.1
  • 69
    • 0002200573 scopus 로고
    • Neue fassung des widerspruchsfreiheitsbeweises fur die reine zahlentheorie
    • Szabo 1969
    • Gentzen, G., 1938. Neue Fassung des Widerspruchsfreiheitsbeweises fur die reine Zahlentheorie. Forschungen zur Logik,4: 19-44. Translated as ‘New version of the consistency proof for elementary number theory’ in Szabo 1969.
    • (1938) Forschungen Zur Logik , vol.4 , pp. 19-44
    • Gentzen, G.1
  • 71
    • 85066359405 scopus 로고
    • On the completeness of the calculus of logic, Gödel 1986
    • Gödel, K., 1929. On the completeness of the calculus of logic. In Gödel 1986, pp. 60-101.
    • (1929) , pp. 60-101
    • Gödel, K.1
  • 72
    • 0009737277 scopus 로고
    • On formally undecidable propositions
    • related systems I, Gödel 1986
    • Gödel, K., 1931. On formally undecidable propositions of Principia Mathematica and related systems I. In Gödel 1986, pp. 144-195.
    • (1931) Principia Mathematica , pp. 144-195
    • Gödel, K.1
  • 73
    • 85066369217 scopus 로고
    • Consistency and completeness, Gödel 1986
    • Gödel, K., 1932. Consistency and completeness. In Gödel 1986, pp. 234-237.
    • (1932) , pp. 234-237
    • Gödel, K.1
  • 74
    • 85066358962 scopus 로고
    • The present situation in the foundations of mathematics, Gödel 1995
    • Gödel, K., 1933. The present situation in the foundations of mathematics. In Gödel 1995, pp. 45-53.
    • (1933) , pp. 45-53
    • Gödel, K.1
  • 75
    • 85066364375 scopus 로고
    • On undecidable propositions of formal mathematical systems, Gödel 1986
    • Gödel, K., 1934. On undecidable propositions of formal mathematical systems. In Gödel 1986, pp. 346-371.
    • (1934) , pp. 346-371
    • Gödel, K.1
  • 76
    • 85066370641 scopus 로고
    • On the length of proofs, Gödel 1986
    • Gödel, K., 1936. On the length of proofs. In Gödel 1986, pp. 396-399.
    • (1936) , pp. 396-399
    • Gödel, K.1
  • 77
    • 85066370643 scopus 로고
    • Some basic theorems on the foundations of mathematics and their implications, Goödel 1995
    • Gödel, K., 1951. Some basic theorems on the foundations of mathematics and their implications. In Goödel 1995, pp. 304-323.
    • (1951) , pp. 304-323
    • Gödel, K.1
  • 78
    • 85066381902 scopus 로고
    • On a hitherto unutilized extension of the finitary standpoint, Gödel 1990
    • Gödel, K., 1958. On a hitherto unutilized extension of the finitary standpoint. In Gödel 1990, pp. 241-251.
    • (1958) , pp. 241-251
    • Gödel, K.1
  • 79
    • 85066362291 scopus 로고
    • Some remarks on the undecidability results, Gödel 1990
    • Gödel, K., 1972. Some remarks on the undecidability results. In Gödel 1990, pp. 305-306.
    • (1972) , pp. 305-306
    • Gödel, K.1
  • 80
    • 0003913615 scopus 로고    scopus 로고
    • New York and Oxford: Oxford University Press
    • Gödel, K., 1986. Collected Works, Vol. 1: Publications 1929-1936.New York and Oxford: Oxford University Press.
    • (1986) Collected Works , vol.1
    • Gödel, K.1
  • 81
    • 0003913615 scopus 로고    scopus 로고
    • New York and Oxford: Oxford University Press
    • Gödel, K., 1990. Collected Works, Vol. 2: Publications 1938-1974.New York and Oxford: Oxford University Press.
    • (1990) Collected Works , vol.2
    • Gödel, K.1
  • 82
    • 0003913615 scopus 로고    scopus 로고
    • Oxford: Clarendon Press
    • Gödel, K., 2003a. Collected Works, Vol. 4: Correspondence A-G.Oxford: Clarendon Press.
    • (2003) Collected Works , vol.4
    • Gödel, K.1
  • 83
    • 0003913615 scopus 로고    scopus 로고
    • Oxford: Clarendon Press
    • Gödel, K., 2003b. Collected Works, Vol. 5: Correspondence H-Z.Oxford: Clarendon Press.
    • (2003) Collected Works , vol.5
    • Gödel, K.1
  • 84
    • 0344955448 scopus 로고    scopus 로고
    • Boca Raton, Florida: Chapman and Hall/CRC
    • Goldrei, D., 1996. Classic Set Theory.Boca Raton, Florida: Chapman and Hall/CRC.
    • (1996) Classic Set Theory
    • Goldrei, D.1
  • 85
    • 33750154539 scopus 로고
    • On the restricted ordinal theorem
    • Goodstein, R. L., 1944. On the restricted ordinal theorem. Journal of Symbolic Logic, 9: 33-41.
    • (1944) Journal of Symbolic Logic , vol.9 , pp. 33-41
    • Goodstein, R.L.1
  • 89
    • 85066381078 scopus 로고    scopus 로고
    • Hart, W. D. (ed.), 1996. The Philosophy of Mathematics.Oxford Readings in Philosophy. Oxford University Press.
    • Hart, W.D.1
  • 90
    • 85066359610 scopus 로고    scopus 로고
    • The logic of frege’s theorem. Forthcoming
    • Crispin Wright
    • Heck, R., 2007. The logic of Frege’s Theorem. Forthcoming in a Festschrift for Crispin Wright.
    • (2007) Festschrift
    • Heck, R.1
  • 91
    • 31344470864 scopus 로고
    • A problem concerning provability
    • Henkin, L., 1952. A problem concerning provability. Journal of Symbolic Logic,17: 160.
    • (1952) Journal of Symbolic Logic , vol.17 , pp. 160
    • Henkin, L.1
  • 92
    • 85066364882 scopus 로고
    • On the infinite, van Heijenoort 1967
    • Hilbert, D., 1925. On the infinite. In van Heijenoort 1967, pp. 369-392.
    • (1925) , pp. 369-392
    • Hilbert, D.1
  • 93
    • 0003879089 scopus 로고
    • Berlin: Springer., 1938, translated, New York: Chesea Publishing Co
    • Hilbert, D. and Ackermann, W., 1928. Grundzüge der theoretischen Logik.Berlin: Springer. 2nd edn. 1938, translated as Principles of Mathematical Logic, New York: Chesea Publishing Co., 1950.
    • (1928) Grundzüge Der Theoretischen Logik , pp. 1950
    • Hilbert, D.1    Ackermann, W.2
  • 96
    • 0003944612 scopus 로고    scopus 로고
    • Cambridge: Cambridge University Press
    • Hodges, W., 1997. A Shorter Model Theory.Cambridge: Cambridge University Press.
    • (1997) A Shorter Model Theory
    • Hodges, W.1
  • 97
    • 1442344282 scopus 로고
    • London: Macmillan
    • Hunter, G., 1971. Metalogic.London: Macmillan.
    • (1971) Metalogic
    • Hunter, G.1
  • 98
    • 52549114807 scopus 로고
    • Arithmetical truth and hidden higher-order concepts
    • The Paris Logic Group, Amsterdam: North-Holland. Page references are to the reprint in Hart 1996
    • Isaacson, D., 1987. Arithmetical truth and hidden higher-order concepts. In The Paris Logic Group (ed.), Logic Colloquium’85.Amsterdam: North-Holland. Page references are to the reprint in Hart 1996.
    • (1987) Logic Colloquium’85
    • Isaacson, D.1
  • 99
    • 84972554351 scopus 로고
    • What evidence is there that 265536 is a natural number?
    • Isles, D., 1992. What evidence is there that 265536 is a natural number?Notre Dame Journal of Formal Logic,33: 465-480.
    • (1992) Notre Dame Journal of Formal Logic , vol.33 , pp. 465-480
    • Isles, D.1
  • 100
    • 33847408236 scopus 로고
    • Redundancies in the hilbert-bernays derivability conditions for gödel’s second incompleteness theorem
    • Jeroslow, R. G., 1973. Redundancies in the Hilbert-Bernays derivability conditions for Gödel’s second incompleteness theorem. Journal of Symbolic Logic,38: 359-367.
    • (1973) Journal of Symbolic Logic , vol.38 , pp. 359-367
    • Jeroslow, R.G.1
  • 101
    • 0003716199 scopus 로고
    • An argument against the plausibility of church’s thesis
    • A. Heyt-ing, Amsterdam: North-Holland
    • Kalmár, L. 1959. An argument against the plausibility of Church’s Thesis. In A. Heyt-ing (ed.), Proceedings of the Colloquium held at Amsterdam, 1957, pp. 72-80. Amsterdam: North-Holland.
    • (1959) Proceedings of the Colloquium Held at Amsterdam, 1957 , pp. 72-80
    • Kalmár, L.1
  • 102
    • 85066365624 scopus 로고
    • Oxford Logic Guides, Oxford: Clarendon Press
    • Kaye, R., 1991. Models of Peemo Arithmetic.Oxford Logic Guides 15. Oxford: Clarendon Press.
    • (1991) Models of Peemo Arithmetic , pp. 15
    • Kaye, R.1
  • 104
    • 0039467481 scopus 로고    scopus 로고
    • Deflationism and tarski’s paradise
    • Ketland, J., 1999. Deflationism and Tarski’s paradise. Mind,108: 69-94.
    • (1999) Mind , vol.108 , pp. 69-94
    • Ketland, J.1
  • 105
    • 35348938172 scopus 로고    scopus 로고
    • Deflationism and the gödel phenomena: Reply to tennant
    • Ketland, J., 2005. Deflationism and the Gödel phenomena: reply to Tennant. Mind, 114: 75-88.
    • (2005) Mind , vol.114 , pp. 75-88
    • Ketland, J.1
  • 107
    • 0001481675 scopus 로고
    • General recursive functions of natural numbers
    • Kleene, S. C., 1936a. General recursive functions of natural numbers. Mathematische Annalen,112: 727-742.
    • (1936) Mathematische Annalen , vol.112 , pp. 727-742
    • Kleene, S.C.1
  • 108
    • 0011261326 scopus 로고
    • A-definability and recursiveness
    • Kleene, S. C., 1936b. A-definability and recursiveness. Duke Mathematical Journal,2: 340-353.
    • (1936) Duke Mathematical Journal , vol.2 , pp. 340-353
    • Kleene, S.C.1
  • 115
    • 0007252614 scopus 로고
    • Does gödel’s theorem matter to mathematics?
    • Also in Harrington et al., 1985
    • Kolata, G., 1982. Does Gödel’s theorem matter to mathematics?Science,218: 779-780. Also in Harrington et al., 1985.
    • (1982) Science , vol.218 , pp. 779-780
    • Kolata, G.1
  • 117
    • 84916234889 scopus 로고
    • Abstract: A refinement of consistency
    • Kreisel, G., 1957. Abstract: A refinement of consistency. Journal of Symbolic Logic, 22: 108-109.
    • (1957) Journal of Symbolic Logic , vol.22 , pp. 108-109
    • Kreisel, G.1
  • 118
    • 0003326043 scopus 로고
    • Mathematical logic
    • T. L. Saaty, New York: John Wiley
    • Kreisel, G., 1965. Mathematical logic. In T. L. Saaty (ed.), Lectures on Modern Mathematics, vol. III, pp. 95-195. New York: John Wiley.
    • (1965) Lectures on Modern Mathematics , vol.3 , pp. 95-195
    • Kreisel, G.1
  • 119
    • 0039777615 scopus 로고
    • Informal rigour and completeness proofs
    • I. Lakatos, Amsterdam: North-Holland
    • Kreisel, G., 1972. Informal rigour and completeness proofs. In I. Lakatos (ed.), Problems in the Philosophy of Mathematics. Amsterdam: North-Holland.
    • (1972) Problems in the Philosophy of Mathematics
    • Kreisel, G.1
  • 121
    • 85066354562 scopus 로고    scopus 로고
    • Kretzmann, N. and Stump, E., 1988. The Cambridge Translations of Medieval Philosophical Texts: Vol. 1, Logic and the Philosophy of Language. Cambridge University Press.
    • Kretzmann, N.1    Stump, E.2
  • 122
  • 124
    • 85066368139 scopus 로고    scopus 로고
    • LindströmP., 2003. Aspects of Incompleteness.A. K. Péters, 2nd edn.
    • Lindström, P.1
  • 125
    • 0007458333 scopus 로고
    • Solution of a problem of leon henkin
    • Löb M. H., 1955. Solution of a problem of Leon Henkin. Journal of Symbolic Logic, 20: 115-118.
    • (1955) Journal of Symbolic Logic , vol.20 , pp. 115-118
    • Löb, M.H.1
  • 126
    • 85066375263 scopus 로고
    • On possibilities in the calculus of relatives, van Heijenoort 1967
    • Löwenheim L., 1915. On possibilities in the calculus of relatives. In van Heijenoort 1967, pp. 232-251.
    • (1915) , pp. 232-251
    • Löwenheim, L.1
  • 127
    • 84971120913 scopus 로고
    • Minds, machines and gödel
    • Lucas, J. R., 1961. Minds, machines and Gödel. Philosophy,36: 112-127.
    • (1961) Philosophy , vol.36 , pp. 112-127
    • Lucas, J.R.1
  • 128
    • 0013059980 scopus 로고    scopus 로고
    • Minds, machines and gödel: A retrospect
    • P. J. R. Millican and A. Clark, Oxford: Oxford University Press
    • Lucas, J. R., 1996. Minds, machines and Gödel: A retrospect. In P. J. R. Millican and A. Clark (eds.), Machines and Thought: The Legacy of Alan Turing.Oxford: Oxford University Press.
    • (1996) Machines and Thought: The Legacy of Alan Turing
    • Lucas, J.R.1
  • 131
    • 61249530800 scopus 로고
    • A homogeneous system for formal logic
    • Martin, R. M., 1943. A homogeneous system for formal logic. Journal of Symbolic Logic, 8: 1-23.
    • (1943) Journal of Symbolic Logic , vol.8 , pp. 1-23
    • Martin, R.M.1
  • 132
    • 61249216997 scopus 로고
    • A note on nominalism and recursive functions
    • Martin, R. M., 1949. A note on nominalism and recursive functions. Journal of Symbolic Logic, 14: 27-31.
    • (1949) Journal of Symbolic Logic , vol.14 , pp. 27-31
    • Martin, R.M.1
  • 133
    • 85066394395 scopus 로고    scopus 로고
    • Mendelson, E., 1964. Introduction to Mathematical Logic.Princeton, NJ: van Nostrand.
    • Mendelson, E.1
  • 134
    • 0013152045 scopus 로고
    • Second thoughts about church’s thesis and mathematical proofs
    • Mendelson, E., 1990. Second thoughts about Church’s thesis and mathematical proofs. Journal of Philosophy,87: 225-233.
    • (1990) Journal of Philosophy , vol.87 , pp. 225-233
    • Mendelson, E.1
  • 136
    • 85066364066 scopus 로고
    • Computational complexity and program structure, Tech. Rep. RC-1817, IBM
    • Meyer, A. R. and Ritchie, D., 1967. Computational complexity and program structure. Tech. Rep. RC-1817, IBM.
    • (1967)
    • Meyer, A.R.1    Ritchie, D.2
  • 137
    • 34447627217 scopus 로고    scopus 로고
    • On goodel sentences and what they say. Forthcoming
    • Milne, P., 2007. On Goodel sentences and what they say. Forthcoming in Philosophia Mathematica.
    • (2007) Philosophia Mathematica
    • Milne, P.1
  • 139
    • 61249742020 scopus 로고
    • A derivation on number theory from ancestral theory
    • Myhill, J., 1952. A derivation on number theory from ancestral theory. Journal of Symbolic Logic,17: 192-197.
    • (1952) Journal of Symbolic Logic , vol.17 , pp. 192-197
    • Myhill, J.1
  • 140
    • 84972502971 scopus 로고
    • Church’s thesis and cognitive science
    • Nelson, R. J., 1987. Church’s Thesis and cognitive science. Notre Dame Journal of Formal Logic, 28: 581-614.
    • (1987) Notre Dame Journal of Formal Logic , vol.28 , pp. 581-614
    • Nelson, R.J.1
  • 143
    • 0001695955 scopus 로고
    • Existence and feasibility in arithmetic
    • Parikh, R., 1971. Existence and feasibility in arithmetic. Journal of Symbolic Logic, 36: 494-508.
    • (1971) Journal of Symbolic Logic , vol.36 , pp. 494-508
    • Parikh, R.1
  • 144
    • 0041484427 scopus 로고
    • The incompleteness theorems
    • J. Barwise, Amsterdam: North-Holland
    • Paris, J. and Harrington, L. A., 1977. The incompleteness theorems. In J. Barwise (ed.), Handbook of Mathematical Logic, pp. 1133-1142. Amsterdam: North-Holland.
    • (1977) Handbook of Mathematical Logic , pp. 1133-1142
    • Paris, J.1    Harrington, L.A.2
  • 146
    • 0009007409 scopus 로고    scopus 로고
    • Finitism and intuitive knowledge
    • M. Schirn, Oxford University Press
    • Parsons, C., 1998. Finitism and intuitive knowledge. In M. Schirn (ed.), The Philosophy of Mathematics Today, chap. 249-270. Oxford University Press.
    • (1998) The Philosophy of Mathematics Today , pp. 249-270
    • Parsons, C.1
  • 149
  • 150
    • 0003172246 scopus 로고
    • Uber den zusammenhang der verschiedenen begriffe der rekursiven funktionen
    • Péter, R., 1934. Uber den Zusammenhang der verschiedenen Begriffe der rekursiven Funktionen. Mathematische Annalen, 110: 612-632.
    • (1934) Mathematische Annalen , vol.110 , pp. 612-632
    • Péter, R.1
  • 151
    • 26344472493 scopus 로고
    • Konstruktion nichtrekursiver funktionen
    • Péter, R., 1935. Konstruktion nichtrekursiver Funktionen. Mathematische Annalen, 111: 42-60.
    • (1935) Mathematische Annalen , vol.111 , pp. 42-60
    • Péter, R.1
  • 152
    • 0013557580 scopus 로고
    • Budapest: Akademiai Kiado. Translated as Péter
    • Péter, R., 1951. Rekursive Funktionen.Budapest: Akademiai Kiado. Translated as Péter 1967.
    • (1951) Rekursive Funktionen , pp. 1967
    • Péter, R.1
  • 154
    • 0002269481 scopus 로고
    • Lecture Notes in Mathematics 1407, Springer-Verlag
    • Pohlers, W., 1989. Proof Theory.Lecture Notes in Mathematics 1407. Springer-Verlag.
    • (1989) Proof Theory
    • Pohlers, W.1
  • 157
    • 0002217486 scopus 로고
    • Uber die vollstandigkeit eines gewisse systems der arithmetik ganzer zahlen
    • welchem die Addition als einzige Operation hervortritt, F. Leja, Translated as Presburger 1991
    • Presburger, M., 1930. Uber die Vollstandigkeit eines gewisse Systems der Arithmetik ganzer Zahlen, in welchem die Addition als einzige Operation hervortritt. In F. Leja (ed.), Comptes-rendus du I Congrès des Mathématiciens des Pays Slaves, Varsovie 1929, pp. 92-101. Translated as Presburger 1991.
    • (1930) Comptes-Rendus Du I Congrès Des Mathématiciens Des Pays Slaves, Varsovie 1929 , pp. 92-101
    • Presburger, M.1
  • 158
    • 0005274623 scopus 로고
    • On the completeness of a certain system of arithmetic of whole numbers in which addition occurs as the only operation
    • Presburger, M., 1991. On the completeness of a certain system of arithmetic of whole numbers in which addition occurs as the only operation. History and Philosophy of Logic, 12: 225-233.
    • (1991) History and Philosophy of Logic , vol.12 , pp. 225-233
    • Presburger, M.1
  • 159
    • 0002648050 scopus 로고    scopus 로고
    • The length of proofs
    • S. R. Buss, Amsterdam: Elsevier Science B.V
    • Pudlák, P., 1998. The length of proofs. In S. R. Buss (ed.), Handbook of Proof Theory, pp. 547-638. Amsterdam: Elsevier Science B.V.
    • (1998) Handbook of Proof Theory , pp. 547-638
    • Pudlák, P.1
  • 160
    • 0002286226 scopus 로고
    • Minds and machines
    • S. Hook, New York: New York University Press. In Putnam 1975
    • Putnam, H., 1960. Minds and machines. In S. Hook (ed.), Dimensions of Mind, pp. 148-179. New York: New York University Press. In Putnam 1975, pp. 362-385.
    • (1960) Dimensions of Mind
    • Putnam, H.1
  • 162
    • 0004225575 scopus 로고
    • Cambridge, MA: Harvard University Press
    • Quine, W. V., 1940. Mathematical Logic.Cambridge, MA: Harvard University Press.
    • (1940) Mathematical Logic
    • Quine, W.V.1
  • 163
    • 58149492900 scopus 로고    scopus 로고
    • Hilbert’s program revisited
    • Raatikainen, P., 2003. Hilbert’s program revisited. Synthese,137: 157-177.
    • (2003) Synthese , vol.137 , pp. 157-177
    • Raatikainen, P.1
  • 164
    • 84960578136 scopus 로고
    • The foundations of mathematics
    • Page references are to the reprint in Ramsey 1990
    • Ramsey, F. P., 1925. The foundations of mathematics.Proceedings of the London Mathematical Society,25: 338-384. Page references are to the reprint in Ramsey 1990.
    • (1925) Proceedings of the London Mathematical Society , vol.25 , pp. 338-384
    • Ramsey, F.P.1
  • 165
    • 0003895373 scopus 로고
    • Cambridge: Cambridge University Press. Edited by D. H. Mellor
    • Ramsey, F. P., 1990. Philosophical Papers.Cambridge: Cambridge University Press. Edited by D. H. Mellor.
    • (1990) Philosophical Papers
    • Ramsey, F.P.1
  • 167
    • 0003164887 scopus 로고
    • Definability and decision problems in arithmetic
    • Robinson, J., 1949. Definability and decision problems in arithmetic. Journal of Symbolic Logic,14: 98-114.
    • (1949) Journal of Symbolic Logic , vol.14 , pp. 98-114
    • Robinson, J.1
  • 169
    • 0002811761 scopus 로고
    • Extensions of some theorems of gödel and church
    • Rosser, J. B., 1936. Extensions of some theorems of Gödel and Church. Journal of Symbolic Logic, 1: 230-235.
    • (1936) Journal of Symbolic Logic , vol.1 , pp. 230-235
    • Rosser, J.B.1
  • 170
    • 85066388560 scopus 로고
    • van Heijenoort 1967
    • Russell, B., 1902. Letter to Frege. In van Heijenoort 1967, pp. 124-125.
    • (1902) , pp. 124-125
    • Russell, B.1
  • 172
    • 0000719960 scopus 로고
    • Mathematical logic as based on the theory of types
    • Reprinted in Russell 1956
    • Russell, B., 1908. Mathematical logic as based on the theory of types. American Journal of Mathematics, 30: 222-262. Reprinted in Russell 1956.
    • (1908) American Journal of Mathematics , vol.30 , pp. 222-262
    • Russell, B.1
  • 174
    • 85066380398 scopus 로고    scopus 로고
    • Russell, B. and Whitehead, A. N., 1910-13. Principia Mathematica.Cambridge: Cambridge University Press.
    • Russell, B.1    Whitehead, A.N.2
  • 175
    • 17144380285 scopus 로고
    • Universelle turing speicherung
    • J. Dorr and G. Hotz, Mannheim: Bibliogr. Institut
    • Schönhage A., 1970. Universelle Turing Speicherung. In J. Dorr and G. Hotz (eds.), Automatentheorie und Formal Sprachen.Mannheim: Bibliogr. Institut.
    • (1970) Automatentheorie Und Formal Sprachen
    • Schönhage, A.1
  • 176
  • 178
    • 0032148332 scopus 로고    scopus 로고
    • Incompleteness, mechanism and optimism
    • Shapiro, S., 1998. Incompleteness, mechanism and optimism. Bulletin of Symbolic Logic, 4: 273-302.
    • (1998) Bulletin of Symbolic Logic , vol.4 , pp. 273-302
    • Shapiro, S.1
  • 179
    • 85066383250 scopus 로고    scopus 로고
    • Computability, proof, and open-texture. In Olszewski et al. (2006)
    • Shapiro, S., 2006a. Computability, proof, and open-texture. In Olszewski et al. (2006), pp. 420-455.
    • (2006) , pp. 420-455
    • Shapiro, S.1
  • 184
    • 0031510755 scopus 로고    scopus 로고
    • Step by recursive step: Church’s analysis of effective calculability
    • Sieg, W., 1997. Step by recursive step: Church’s analysis of effective calculability. Bulletin of Symbolic Logic, 3: 154-180.
    • (1997) Bulletin of Symbolic Logic , vol.3 , pp. 154-180
    • Sieg, W.1
  • 187
    • 85066366062 scopus 로고
    • The foundations of elementary arithmetic established by means of the recursive mode of thought, without the use of apparent variables ranging over infinite domains. In van Heijenoort 1967
    • Skolem, T., 1923. The foundations of elementary arithmetic established by means of the recursive mode of thought, without the use of apparent variables ranging over infinite domains. In van Heijenoort 1967, pp. 303-333.
    • (1923) , pp. 303-333
    • Skolem, T.1
  • 190
    • 0348174110 scopus 로고
    • The incompleteness theorems
    • J. Barwise, Amsterdam: North-Holland
    • Smoryński C., 1977. The incompleteness theorems. In J. Barwise (ed.), Handbook of Mathematical Logic, pp. 821-865. Amsterdam: North-Holland.
    • (1977) Handbook of Mathematical Logic , pp. 821-865
    • Smoryński, C.1
  • 191
    • 0346439775 scopus 로고
    • The varieties of arboreal experience
    • Also in Harrington et al., 1985
    • Smoryński C., 1982. The varieties of arboreal experience. Mathematical Intelligencer,4: 182-189. Also in Harrington et al., 1985.
    • (1982) Mathematical Intelligencer , vol.4 , pp. 182-189
    • Smoryński, C.1
  • 195
    • 27744602784 scopus 로고
    • Cambridge: Cambridge University Press
    • Steen, S. W. P., 1972. Mathematical Logic.Cambridge: Cambridge University Press.
    • (1972) Mathematical Logic
    • Steen, S.1
  • 197
    • 0347786825 scopus 로고
    • Finitism
    • Reprinted in Tait 2005
    • Tait, W. W., 1981. Finitism. Journal of Philosophy,78: 524-546. Reprinted in Tait 2005.
    • (1981) Journal of Philosophy , vol.78 , pp. 524-546
    • Tait, W.W.1
  • 198
    • 84894324149 scopus 로고    scopus 로고
    • Remarks on finitism
    • W. Sieg, R. Sommer, and C. Talcott, Association for Symbolic Logic and A K Péters. Reprinted in Tait 2005
    • Tait, W. W., 2002. Remarks on finitism. In W. Sieg, R. Sommer, and C. Talcott (eds.), Reflections on the Foundations of Mathematics: Essays in Honor of Solomon Feferman, pp. 410-419. Association for Symbolic Logic and A K Péters. Reprinted in Tait 2005.
    • (2002) Reflections on the Foundations of Mathematics: Essays in Honor of Solomon Feferman , pp. 410-419
    • Tait, W.W.1
  • 200
    • 0003826898 scopus 로고
    • Amsterdam: North-Holland
    • Takeuti, G., 1987. Proof Theory.Amsterdam: North-Holland.
    • (1987) Proof Theory
    • Takeuti, G.1
  • 204
    • 33644701914 scopus 로고
    • Edinburgh: Edinburgh University Press
    • Tennant, N., 1978. Natural Logic.Edinburgh: Edinburgh University Press.
    • (1978) Natural Logic
    • Tennant, N.1
  • 205
    • 33745742790 scopus 로고    scopus 로고
    • Deflationism and the gödel phenomena
    • Tennant, N., 2002. Deflationism and the Gödel phenomena. Mind,111: 551-582.
    • (2002) Mind , vol.111 , pp. 551-582
    • Tennant, N.1
  • 206
    • 61449453757 scopus 로고    scopus 로고
    • Deflationism and the gödel phenomena: Reply to ketland
    • Tennant, N., 2005. Deflationism and the Gödel phenomena: reply to Ketland. Mind, 114: 89-96.
    • (2005) Mind , vol.114 , pp. 89-96
    • Tennant, N.1
  • 207
    • 85066364462 scopus 로고    scopus 로고
    • Tourlakis, G., 2002. A programming formalism for PR.www.cs.yorku.ca/Ggt/papers/loop-programs.ps.
    • Tourlakis, G.1
  • 209
    • 49949118252 scopus 로고
    • Comparing the church and turing approaches: Two prophetical messages
    • Oxford University Press
    • Trakhtenbrot, B. A., 1988. Comparing the Church and Turing approaches: two prophetical messages. In R. Herken (ed.), The Universal Turing Machine, pp. 603-630. Oxford University Press.
    • (1988) The Universal Turing Machine , pp. 603-630
    • Trakhtenbrot, B.A.1
  • 213
    • 84972511093 scopus 로고
    • Peano’s smart children: A provability logical study of systems with built-in consistency
    • Visser, A., 1989. Peano’s smart children: a provability logical study of systems with built-in consistency. Notre Dame Journal of Formal Logic,30: 161-196.
    • (1989) Notre Dame Journal of Formal Logic , vol.30 , pp. 161-196
    • Visser, A.1
  • 214
  • 216
    • 85066387160 scopus 로고    scopus 로고
    • Wang, H., 1974. From Mathematics to Philosophy.Routledge and Kegan Paul.
    • Wang, H.1
  • 217
    • 38249037032 scopus 로고
    • On the scheme of induction for bounded arithmetic formulas
    • Wilkie, A. J. and Paris, J., 1987. On the scheme of induction for bounded arithmetic formulas. Annals of Pure and Applied Logic, 35: 261-302.
    • (1987) Annals of Pure and Applied Logic , vol.35 , pp. 261-302
    • Wilkie, A.J.1    Paris, J.2
  • 218
    • 0035534323 scopus 로고    scopus 로고
    • Self-verifying axiom systems, the incompleteness theorem, and related reflection principles
    • Willard, D. E., 2001. Self-verifying axiom systems, the incompleteness theorem, and related reflection principles. Journal of Symbolic Logic,66: 536-596.
    • (2001) Journal of Symbolic Logic , vol.66 , pp. 536-596
    • Willard, D.E.1
  • 220
    • 0005349856 scopus 로고
    • New York and Oxford: Oxford University Press
    • Yaqub, A., 1993. The Liar Speaks the Truth.New York and Oxford: Oxford University Press.
    • (1993) The Liar Speaks the Truth
    • Yaqub, A.1
  • 221
    • 85066361941 scopus 로고    scopus 로고
    • Zach, R., 2003. Hilbert’s program. In E. N. Zalta (ed.), The Stanford Encyclopedia of Philosophy. URL http://plato.stanford.edu/archives/fall2003/entries/hilbert-program/.
    • Zach, R.1
  • 223
    • 85133469027 scopus 로고    scopus 로고
    • Hilbert’s program then and now
    • D. Jacquette, Amsterdam: North-Holland
    • Zach, R., 2006. Hilbert’s program then and now. In D. Jacquette (ed.), Philosophy of Logic. Amsterdam: North-Holland.
    • (2006) Philosophy of Logic
    • Zach, R.1


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