-
1
-
-
85066357221
-
-
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
-
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
-
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
-
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
-
-
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
-
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
-
-
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
-
-
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
-
13
-
-
0003773186
-
-
Cambridge: Cambridge University Press
-
Boolos, G., Burgess, J., and Jeffrey, R., 2002. Computability and Logic.Cambridge: Cambridge University Press, 4th edn.
-
(2002)
Computability and Logic
-
-
Boolos, G.1
Burgess, J.2
Jeffrey, R.3
-
15
-
-
0009627186
-
-
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
-
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
-
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
-
-
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
-
-
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
-
-
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
-
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
-
-
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
-
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
-
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
-
-
Cambridge: Cambridge University Press
-
Cutland, N. J., 1980. Computability.Cambridge: Cambridge University Press.
-
(1980)
Computability
-
-
Cutland, N.J.1
-
37
-
-
49049136430
-
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
-
-
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
-
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
-
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
-
-
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
-
-
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
-
-
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
-
-
Frege, G., 1950. The Foundations of Arithmetic. Basil Blackwell.
-
-
-
Frege, G.1
-
60
-
-
0039349530
-
-
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
-
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
-
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
-
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
-
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
-
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
-
-
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
-
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
-
-
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
-
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
-
-
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
-
-
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
-
-
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
-
-
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
-
-
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
-
-
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
-
-
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
-
-
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
-
-
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
-
-
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
-
-
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
-
-
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
-
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
-
-
Hart, W. D. (ed.), 1996. The Philosophy of Mathematics.Oxford Readings in Philosophy. Oxford University Press.
-
-
-
Hart, W.D.1
-
90
-
-
85066359610
-
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
-
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
-
-
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
-
-
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
-
-
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
-
-
London: Macmillan
-
Hunter, G., 1971. Metalogic.London: Macmillan.
-
(1971)
Metalogic
-
-
Hunter, G.1
-
98
-
-
52549114807
-
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
-
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
-
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
-
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
-
-
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
-
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
-
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
-
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
-
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
-
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
-
116
-
-
0344991155
-
On the definition of an algorithm
-
Kolmogorov, A. N. and Uspenskii, V. A., 1963. On the definition of an algorithm. American, Mathematical Society Translations,29: 217-245.
-
(1963)
American, Mathematical Society Translations
, vol.29
, pp. 217-245
-
-
Kolmogorov, A.N.1
Uspenskii, V.A.2
-
117
-
-
84916234889
-
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
-
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
-
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
-
-
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
-
-
0004229474
-
-
Cambridge: Cambridge University Press
-
Lakatos, I., 1976. Proofs and Refutations.Cambridge: Cambridge University Press.
-
(1976)
Proofs and Refutations
-
-
Lakatos, I.1
-
124
-
-
85066368139
-
-
LindströmP., 2003. Aspects of Incompleteness.A. K. Péters, 2nd edn.
-
-
-
Lindström, P.1
-
125
-
-
0007458333
-
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
-
-
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
-
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
-
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
-
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
-
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
-
-
Mendelson, E., 1964. Introduction to Mathematical Logic.Princeton, NJ: van Nostrand.
-
-
-
Mendelson, E.1
-
134
-
-
0013152045
-
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
-
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
-
0004112412
-
-
Oxford: Oxford University Press
-
Penrose, R., 1994. Shadows of the Mind,.Oxford: Oxford University Press.
-
(1994)
Shadows of the Mind
-
-
Penrose, R.1
-
150
-
-
0003172246
-
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
-
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
-
-
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
-
-
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
-
155
-
-
33751195485
-
-
Oxford: Oxford University Press
-
Potter, M., 2000. Reason’s Nearest Kin.Oxford: Oxford University Press.
-
(2000)
Reason’s Nearest Kin
-
-
Potter, M.1
-
157
-
-
0002217486
-
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
-
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
-
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
-
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
-
-
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
-
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
-
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
-
-
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
-
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
-
168
-
-
0010047294
-
An essentially undecidable axiom system
-
Providence, R.I
-
Robinson, R., 1952. An essentially undecidable axiom system. In Proceedings of the International Congress of Mathematicians, Cambridge, Mass., 1950, Vol. 1, pp. 729-730. Providence, R.I.
-
(1952)
Proceedings of the International Congress of Mathematicians, Cambridge, Mass., 1950
, vol.1
, pp. 729-730
-
-
Robinson, R.1
-
169
-
-
0002811761
-
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
-
-
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
-
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
-
-
Russell, B. and Whitehead, A. N., 1910-13. Principia Mathematica.Cambridge: Cambridge University Press.
-
-
-
Russell, B.1
Whitehead, A.N.2
-
175
-
-
17144380285
-
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
-
-
0000371259
-
Storage modification machines
-
Schönhage A., 1980. Storage modification machines. SIAM Journal on Computing,9: 490-508.
-
(1980)
SIAM Journal on Computing
, vol.9
, pp. 490-508
-
-
Schönhage, A.1
-
178
-
-
0032148332
-
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
-
-
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
-
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
-
-
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
-
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
-
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
-
-
Cambridge: Cambridge University Press
-
Steen, S. W. P., 1972. Mathematical Logic.Cambridge: Cambridge University Press.
-
(1972)
Mathematical Logic
-
-
Steen, S.1
-
197
-
-
0347786825
-
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
-
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
-
-
Amsterdam: North-Holland
-
Takeuti, G., 1987. Proof Theory.Amsterdam: North-Holland.
-
(1987)
Proof Theory
-
-
Takeuti, G.1
-
204
-
-
33644701914
-
-
Edinburgh: Edinburgh University Press
-
Tennant, N., 1978. Natural Logic.Edinburgh: Edinburgh University Press.
-
(1978)
Natural Logic
-
-
Tennant, N.1
-
205
-
-
33745742790
-
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
-
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
-
-
Tourlakis, G., 2002. A programming formalism for PR.www.cs.yorku.ca/Ggt/papers/loop-programs.ps.
-
-
-
Tourlakis, G.1
-
209
-
-
49949118252
-
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
-
212
-
-
0003691342
-
-
Cambridge, MA: Harvard University Press
-
van Heijenoort, J. (ed.), 1967. From Frege to Gödel.Cambridge, MA: Harvard University Press.
-
(1967)
From Frege to Gödel
-
-
van Heijenoort, J.1
-
213
-
-
84972511093
-
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
-
216
-
-
85066387160
-
-
Wang, H., 1974. From Mathematics to Philosophy.Routledge and Kegan Paul.
-
-
-
Wang, H.1
-
217
-
-
38249037032
-
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
-
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
-
-
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
-
-
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
-
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
|