메뉴 건너뛰기




Volumn 53, Issue 1-2, 2000, Pages 63-96

Does reductive proof theory have a viable rationale?

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0010736859     PISSN: 01650106     EISSN: 15728420     Source Type: Journal    
DOI: 10.1023/a:1005622403850     Document Type: Article
Times cited : (28)

References (50)
  • 1
    • 79959388597 scopus 로고
    • The type theoretic interpretation of constructive set theory
    • A. MacIntyre et al. (eds), North-Holland, Amsterdam
    • Aczel, P.: 1978, 'The Type Theoretic Interpretation of Constructive Set Theory', in A. MacIntyre et al. (eds), Logic Colloquium '77, North-Holland, Amsterdam, pp. 55-66.
    • (1978) Logic Colloquium '77 , pp. 55-66
    • Aczel, P.1
  • 4
    • 0003825031 scopus 로고
    • Benacerraf, P. and H. Putnam eds. Cambridge University Press, Cambridge, U.K.
    • Benacerraf, P. and H. Putnam eds.: 1983, Philosophy of Mathematics, 2nd edn. Cambridge University Press, Cambridge, U.K.
    • (1983) Philosophy of Mathematics, 2nd Edn.
  • 5
    • 33845548283 scopus 로고
    • Notation system for infinitary derivations
    • Buchholz, W.: 1991, 'Notation System for Infinitary Derivations', Archive for Mathematical Logic 30, 277-96.
    • (1991) Archive for Mathematical Logic , vol.30 , pp. 277-296
    • Buchholz, W.1
  • 6
    • 84947943291 scopus 로고    scopus 로고
    • Explaining Gentzen's consistency proof within infinitary proof theory
    • Lecture Notes in Computer Science 1289
    • Buchholz, W.: 1997, 'Explaining Gentzen's Consistency Proof within Infinitary Proof Theory', in KGC'97, Lecture Notes in Computer Science 1289, pp. 4-17.
    • (1997) KGC'97 , pp. 4-17
    • Buchholz, W.1
  • 7
    • 52849116002 scopus 로고    scopus 로고
    • Explaining the Gentzen-Takeuti reduction steps: A second order system
    • Preprint; to appear
    • Buchholz, W.: 1999, 'Explaining the Gentzen-Takeuti Reduction Steps: A Second Order System', Preprint; to appear in Archive for Mathematical Logic.
    • (1999) Archive for Mathematical Logic
    • Buchholz, W.1
  • 9
    • 0008101631 scopus 로고    scopus 로고
    • Buss, S. R. ed., North-Holland, Amsterdam
    • Buss, S. R. ed.: 1998, Handbook of Proof Theory, North-Holland, Amsterdam.
    • (1998) Handbook of Proof Theory
  • 10
    • 0004131230 scopus 로고
    • Harvard University Press, Cambridge
    • Dupre, J.: 1993, The Disorder of Things, Harvard University Press, Cambridge.
    • (1993) The Disorder of Things
    • Dupre, J.1
  • 11
    • 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
  • 12
    • 0002293333 scopus 로고
    • A language and axioms for explicit mathematics
    • J. N. Crossley ed., Lecture Notes in Mathematics
    • Feferman, S.: 1975, A Language and Axioms for Explicit Mathematics', in J. N. Crossley ed., Algebra and Logic, Vol. 450, Lecture Notes in Mathematics, pp. 87-139.
    • (1975) Algebra and Logic , vol.450 , pp. 87-139
    • Feferman, S.1
  • 13
    • 0039013047 scopus 로고
    • Constructive theories of functions and classes
    • M. Boffa et al. (eds), North-Holland, Amsterdam
    • Feferman, S.: 1979, 'Constructive Theories of Functions and Classes', in M. Boffa et al. (eds), Logic Colloquium '78, North-Holland, Amsterdam, pp. 159-224.
    • (1979) Logic Colloquium '78 , pp. 159-224
    • Feferman, S.1
  • 14
    • 52849100315 scopus 로고
    • Foundational ways
    • W. Jager et al. (eds), Birkhauser, Basel. Reprinted in Feferman, 94-104
    • Feferman, S.: 1984, Foundational Ways, in W. Jager et al. (eds), Perspectives in Mathematics, Birkhauser, Basel, pp. 147-85. Reprinted in Feferman 1998, 94-104.
    • (1984) Perspectives in Mathematics , pp. 147-185
    • Feferman, S.1
  • 15
    • 0001112280 scopus 로고
    • Hilbert's program relativized. Proof-theoretical and foundational reductions
    • Feferman, S.: 1988, 'Hilbert's Program Relativized. Proof-Theoretical and Foundational Reductions', J. Symbolic Logic 53, 364-84.
    • (1988) J. Symbolic Logic , vol.53 , pp. 364-384
    • Feferman, S.1
  • 16
    • 52849134652 scopus 로고
    • What rests on what? The proof-theoretical analysis of mathematics
    • J. Czermak, (ed.), Verlag-Holder-Pichler-Tempsky, Vienna. Reprinted in Feferman, 187-208
    • Feferman, S.: 1993, 'What Rests on What? The Proof-Theoretical Analysis of Mathematics', in J. Czermak, (ed.), Philosophy of Mathematics, Vol. I, Verlag-Holder-Pichler-Tempsky, Vienna, pp. 147-71. Reprinted in Feferman 1998, 187-208.
    • (1993) Philosophy of Mathematics , vol.1 , pp. 147-171
    • Feferman, S.1
  • 17
    • 2442552587 scopus 로고    scopus 로고
    • Kreisel's "unwinding" program
    • P. Odifreddi (ed.), A. K. Peters Ltd., Wellesley
    • Feferman, S.: 1996, 'Kreisel's "Unwinding" Program', in P. Odifreddi (ed.), Kreiseliana, A. K. Peters Ltd., Wellesley, pp. 247-73.
    • (1996) Kreiseliana , pp. 247-273
    • Feferman, S.1
  • 19
    • 0033483582 scopus 로고    scopus 로고
    • Does mathematics need new axioms?
    • Feferman, S.: 1999, 'Does Mathematics Need New Axioms?', American Mathematical Monthly 106, 99-111.
    • (1999) American Mathematical Monthly , vol.106 , pp. 99-111
    • Feferman, S.1
  • 20
    • 0041191773 scopus 로고
    • The consistency of elementary number theory
    • M. E. Szabo (ed.), North-Holland, Amsterdam
    • Gentzen, G.: 1969, in M. E. Szabo (ed.), 'The Consistency of Elementary Number Theory',The Collected Papers of Gerhard Gentzen, North-Holland, Amsterdam.
    • (1969) The Collected Papers of Gerhard Gentzen
    • Gentzen, G.1
  • 23
    • 77956962042 scopus 로고
    • Models, translations and interpretations
    • Th. Skolem et al. (eds), North-Holland, Amsterdam
    • Kreisel, G.: 1955, 'Models, Translations and Interpretations', in Th. Skolem et al. (eds), Mathematical Interpretation of Formal Systems, North-Holland, Amsterdam, pp. 26-50.
    • (1955) Mathematical Interpretation of Formal Systems , pp. 26-50
    • Kreisel, G.1
  • 24
    • 84977259221 scopus 로고
    • Hilbert's programme
    • Revised, with Postscript in Benaceraff and Putnam, pp. 207-238
    • Kreisel, G.: 1958, 'Hilbert's Programme', Dialectica 12, 346-72. Revised, with Postscript in Benaceraff and Putnam 1983, pp. 207-238.
    • (1958) Dialectica , vol.12 , pp. 346-372
    • Kreisel, G.1
  • 25
    • 0007375686 scopus 로고
    • A survey of proof theory
    • Kreisel, G.: 1968, A Survey of Proof Theory', J. Symbolic Logic 33, 321-88.
    • (1968) J. Symbolic Logic , vol.33 , pp. 321-388
    • Kreisel, G.1
  • 27
    • 52849116311 scopus 로고    scopus 로고
    • Interpretability in reflexive theories - A survey
    • Lindström, P.: 1997, 'Interpretability in Reflexive Theories - A Survey', Theoria 63(3), 182-209.
    • (1997) Theoria , vol.63 , Issue.3 , pp. 182-209
    • Lindström, P.1
  • 31
    • 0002590912 scopus 로고
    • The unity of science as a working hypothesis
    • H. Feigl et al. (eds), University of Minnesota Press, Minneapolis
    • Oppenheim, P. and H. Putnam: 1958, 'The Unity of Science as a Working Hypothesis', in H. Feigl et al. (eds), Minnesota Studies in the Philosophy of Science, Vol. 2, University of Minnesota Press, Minneapolis.
    • (1958) Minnesota Studies in the Philosophy of Science , vol.2
    • Oppenheim, P.1    Putnam, H.2
  • 32
    • 77956955085 scopus 로고
    • On a number-theoretic choice scheme and its relation to induction
    • A. Kino et al. (eds), North-Holland, Amsterdam
    • Parsons, C.: 1970, 'On a Number-Theoretic Choice Scheme and its Relation to Induction', in A. Kino et al. (eds), Intuitionism and Proof Theory, North-Holland, Amsterdam, pp. 459-473.
    • (1970) Intuitionism and Proof Theory , pp. 459-473
    • Parsons, C.1
  • 34
    • 0009374054 scopus 로고
    • Deduction-preserving "recursive isomorphisms" between theories
    • Pour-El, M. B. and S. Kripke: 1967, 'Deduction-Preserving "Recursive Isomorphisms" between Theories', Fundamenta Mathematicae 61, 141-63.
    • (1967) Fundamenta Mathematicae , vol.61 , pp. 141-163
    • Pour-El, M.B.1    Kripke, S.2
  • 35
    • 0000525758 scopus 로고
    • Proof-theoretic analysis of KPM
    • Rathjen, M.: 1991, 'Proof-Theoretic Analysis of KPM', Archive for Mathematical Logic 30, 377-403.
    • (1991) Archive for Mathematical Logic , vol.30 , pp. 377-403
    • Rathjen, M.1
  • 37
    • 84974065271 scopus 로고
    • Recent advances in ordinal analysis: Ni-CA and related systems
    • Rathjen, M.: 1995, 'Recent Advances in Ordinal Analysis: ni-CA and Related Systems', Bull. Symbolic Logic 1, 468-485.
    • (1995) Bull. Symbolic Logic , vol.1 , pp. 468-485
    • Rathjen, M.1
  • 38
    • 52849097687 scopus 로고    scopus 로고
    • The superjump in Martin-Löf type theory
    • Lecture Notes in Logic
    • Rathjen, M.: 1998, 'The Superjump in Martin-Löf Type Theory', in Proceedings of the Logic Colloquium '98, Lecture Notes in Logic, 13.
    • (1998) Proceedings of the Logic Colloquium '98 , pp. 13
    • Rathjen, M.1
  • 39
  • 40
  • 41
    • 84949250380 scopus 로고    scopus 로고
    • Extending Martin-Löf type theory by One Mahlo universe
    • Preprint; to appear
    • Setzer, A.: 1998, 'Extending Martin-Löf Type Theory by One Mahlo Universe', Preprint; to appear in Archive for Mathematical Logic.
    • (1998) Archive for Mathematical Logic
    • Setzer, A.1
  • 42
    • 0000920466 scopus 로고
    • Partial realizations of Hilbert's program
    • Simpson, S.: 1988, 'Partial Realizations of Hilbert's Program', J. Symbolic Logic 53, 349-63.
    • (1988) J. Symbolic Logic , vol.53 , pp. 349-363
    • Simpson, S.1
  • 44
    • 0347786825 scopus 로고
    • Finitism
    • Tait, W. W.: 1981, 'Finitism', J. Philosophy 78, 524-46.
    • (1981) J. Philosophy , vol.78 , pp. 524-546
    • Tait, W.W.1
  • 45
    • 0003826898 scopus 로고
    • North-Holland, Amsterdam
    • Takeuti, G.: 1975, Proof Theory, North-Holland, Amsterdam.
    • (1975) Proof Theory
    • Takeuti, G.1
  • 49
    • 52849136182 scopus 로고
    • Arithmetic translations of axiom systems
    • Wang, H.: 1951, Arithmetic Translations of Axiom Systems', Transactions American Math. Soc. 71, 283-93.
    • (1951) Transactions American Math. Soc. , vol.71 , pp. 283-293
    • Wang, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.