메뉴 건너뛰기




Volumn 53, Issue 1-2, 2000, Pages 27-61

On the logic of reducibility: Axioms and examples

Author keywords

[No Author keywords available]

Indexed keywords


EID: 33748269931     PISSN: 01650106     EISSN: 15728420     Source Type: Journal    
DOI: 10.1023/a:1005692729370     Document Type: Article
Times cited : (19)

References (52)
  • 2
    • 33748266742 scopus 로고
    • The foundations of rigid body mechanics and the derivation of its laws from those of particle mechanics
    • Henkin, Suppes, Tarski (eds), North-Holland, Amsterdam
    • Adams, E.: 1959, 'The Foundations of Rigid Body Mechanics and the Derivation of its Laws from Those of Particle Mechanics', in Henkin, Suppes, Tarski (eds), The Axiomatic Method, North-Holland, Amsterdam.
    • (1959) The Axiomatic Method
    • Adams, E.1
  • 5
    • 51249186304 scopus 로고
    • A mathematical characterization of interpretation between theories
    • Benthem van, J. and D. Pearce: 1984, 'A Mathematical Characterization of Interpretation between Theories', Studia Logica 43, 295-303.
    • (1984) Studia Logica , vol.43 , pp. 295-303
    • Benthem Van, J.1    Pearce, D.2
  • 6
    • 0010677715 scopus 로고
    • The interpretability logic of Peano arithmetic
    • Berarducci, A.: 1990, 'The Interpretability Logic of Peano Arithmetic', Journal of Symbolic Logic 55, 1059-1089.
    • (1990) Journal of Symbolic Logic , vol.55 , pp. 1059-1089
    • Berarducci, A.1
  • 10
    • 52849123432 scopus 로고
    • Replacing one theory by another under preservation of a given feature
    • Eberle, R.: 1971, 'Replacing One Theory by Another under Preservation of a Given Feature', Philosophy of Science 38, 486-501.
    • (1971) Philosophy of Science , vol.38 , pp. 486-501
    • Eberle, R.1
  • 11
    • 0002092865 scopus 로고
    • Arithmetization of metamathematics in a general setting
    • Feferman, S.: 1960, 'Arithmetization of Metamathematics in a General Setting', Fundamenta Mathematicae XLIX, 35-92.
    • (1960) Fundamenta Mathematicae , vol.49 , pp. 35-92
    • Feferman, S.1
  • 12
    • 0001112280 scopus 로고
    • Hilbert's program relativized: Proof-theoretical and foundational reductions
    • Feferman, S.: 1988, 'Hilbert's Program Relativized: Proof-Theoretical and Foundational Reductions', Journal of Symbolic Logic 53, 364-384.
    • (1988) Journal of Symbolic Logic , vol.53 , pp. 364-384
    • Feferman, S.1
  • 13
    • 52849134652 scopus 로고
    • What rests on what? The proof-theoretic analysis of mathematics
    • J. Czermak (ed.), Akten des 15. Internationalen Wittgenstein-Symposiums, Holder-Pichler-Tempsky, Wien
    • Feferman, S.: 1993, 'What Rests on What? The Proof-Theoretic Analysis of Mathematics', in J. Czermak (ed.), Philosophie der Mathematik, Akten des 15. Internationalen Wittgenstein-Symposiums, Holder-Pichler-Tempsky, Wien, pp. 147-171.
    • (1993) Philosophie der Mathematik , pp. 147-171
    • Feferman, S.1
  • 15
    • 34248877666 scopus 로고
    • A note on syntactical and semantical functions
    • Gajda, A., M. Krynicki, and L. Szczerba: 1987, 'A Note on Syntactical and Semantical Functions', Studia Logica 46, 177-185.
    • (1987) Studia Logica , vol.46 , pp. 177-185
    • Gajda, A.1    Krynicki, M.2    Szczerba, L.3
  • 16
    • 34250088481 scopus 로고
    • The adequacy condition as a definition of elementary interpretation
    • Gajda, A.: 1988, 'The Adequacy Condition as a Definition of Elementary Interpretation', Studia Logica 47, 57-69.
    • (1988) Studia Logica , vol.47 , pp. 57-69
    • Gajda, A.1
  • 17
    • 34347193348 scopus 로고
    • Über formal unentscheidbare sätze der principia mathematica und verwandter systeme I
    • Gödel: 1931, 'Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I', Monatshefte für Mathematik und Physik 38, 173-198.
    • (1931) Monatshefte für Mathematik und Physik , vol.38 , pp. 173-198
    • Gödel1
  • 18
    • 52849122538 scopus 로고
    • On interpretability in theories containing arithmetic
    • Hájek, P. and M. Hájkova: 1972, 'On Interpretability in Theories Containing Arithmetic', Fundamenta Mathematicae 76, 131-137.
    • (1972) Fundamenta Mathematicae , vol.76 , pp. 131-137
    • Hájek, P.1    Hájkova, M.2
  • 20
    • 0000031141 scopus 로고
    • Physicalism: Ontology, determination, and reduction
    • Hellman, G. and F. W. Thompson: 1975, 'Physicalism: Ontology, Determination, and Reduction', Journal of Philosophy 72, 551-564.
    • (1975) Journal of Philosophy , vol.72 , pp. 551-564
    • Hellman, G.1    Thompson, F.W.2
  • 21
    • 84958439061 scopus 로고
    • Towards a general theory of reduction
    • Hooker, C.: 1981, 'Towards a General Theory of Reduction', Dialogue XX, 1-3, 38-59, 201-236, 496-529.
    • (1981) Dialogue , vol.20 , pp. 1-3
    • Hooker, C.1
  • 22
    • 0010673986 scopus 로고
    • Provability logics for relative interpretability
    • P. P. Petkov (ed.), Plenum Press, New York
    • Jongh de, D. and F. Veltman: 1990, 'Provability Logics for Relative Interpretability', in P. P. Petkov (ed.), Mathematical Logic, Plenum Press, New York, pp. 31-42.
    • (1990) Mathematical Logic , pp. 31-42
    • Jongh De, D.1    Veltman, F.2
  • 24
    • 0007375686 scopus 로고
    • A survey of proof theory
    • Kreisel, G.: 1968, 'A Survey of Proof Theory', Journal of Symbolic Logic 33, 321-388.
    • (1968) Journal of Symbolic Logic , vol.33 , pp. 321-388
    • Kreisel, G.1
  • 26
    • 0004279221 scopus 로고
    • North-Holland, Amsterdam
    • Kunen, K.: 1980, Set Theory, North-Holland, Amsterdam.
    • (1980) Set Theory
    • Kunen, K.1
  • 28
    • 52849084502 scopus 로고
    • On faithful interpretability
    • M. Richter et.al. (eds), Springer, Berlin
    • Lindström, P.: 1984a, 'On Faithful Interpretability', in M. Richter et.al. (eds), Logic Colloquium '83, Springer, Berlin, pp. 279-288.
    • (1984) Logic Colloquium '83 , pp. 279-288
    • Lindström, P.1
  • 29
    • 84972506724 scopus 로고
    • On certain lattices of degrees of interpretability
    • Lindström, P.: 1984b, 'On Certain Lattices of Degrees of Interpretability', Notre Dame Journal of Formal Logic 25, 127-140.
    • (1984) Notre Dame Journal of Formal Logic , vol.25 , pp. 127-140
    • Lindström, P.1
  • 31
    • 77957664229 scopus 로고
    • General logics
    • H. D. Ebbinghaus et al. (eds), Springer, Berlin
    • Meseguer, J.: 1989, 'General Logics', in H. D. Ebbinghaus et al. (eds), Logic Colloquium '87, Springer, Berlin, pp. 275-329.
    • (1989) Logic Colloquium '87 , pp. 275-329
    • Meseguer, J.1
  • 32
    • 32244444065 scopus 로고
    • Theories incomparable with respect to relative interpretability
    • Montague, R.: 1962, 'Theories Incomparable with Respect to Relative Interpretability', Journal of Symbolic Logic 27, 195-211.
    • (1962) Journal of Symbolic Logic , vol.27 , pp. 195-211
    • Montague, R.1
  • 33
    • 52849093087 scopus 로고
    • Interpretability in terms of models
    • Montague, R.: 1965, 'Interpretability in Terms of Models', Indagationes Mathematicae 27, 467-476.
    • (1965) Indagationes Mathematicae , vol.27 , pp. 467-476
    • Montague, R.1
  • 34
    • 52849113094 scopus 로고
    • A lattice of interpretability types of theories
    • Mycielski, J.: 1977, 'A Lattice of Interpretability Types of Theories', Journal of Symbolic Logic 42, 297-305.
    • (1977) Journal of Symbolic Logic , vol.42 , pp. 297-305
    • Mycielski, J.1
  • 36
    • 84944815311 scopus 로고
    • Relative interpretations
    • Orey, S.: 1961, 'Relative Interpretations', Journal of Symbolic Logic 7, 146-153.
    • (1961) Journal of Symbolic Logic , vol.7 , pp. 146-153
    • Orey, S.1
  • 37
    • 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, 141-163.
    • (1967) Fundamenta Mathematicae , vol.61 , pp. 141-163
    • Pour-El, M.B.1    Kripke, S.2
  • 38
    • 32244444676 scopus 로고
    • Some prime elements in the lattice of interpretability types
    • Pudlák, P.: 1983, 'Some Prime Elements in the Lattice of Interpretability Types', Transactions of the American Mathematical Society 280, 255-275.
    • (1983) Transactions of the American Mathematical Society , vol.280 , pp. 255-275
    • Pudlák, P.1
  • 39
    • 0000889550 scopus 로고
    • Cuts, consistency statements and interpretability
    • Pudlák, P.: 1985, 'Cuts, Consistency Statements and Interpretability', Journal of Symbolic Logic 50, 423-441.
    • (1985) Journal of Symbolic Logic , vol.50 , pp. 423-441
    • Pudlák, P.1
  • 40
    • 0000356439 scopus 로고
    • Approaches to reduction
    • Schaffner, K.: 1967, 'Approaches to Reduction', Philosophy of Science 34, 137-147.
    • (1967) Philosophy of Science , vol.34 , pp. 137-147
    • Schaffner, K.1
  • 41
    • 52849097689 scopus 로고
    • Reduction, representation and commensurability of theories
    • Schroeder-Heister, P. and F. Schaefer: 1989, 'Reduction, Representation and Commensurability of Theories', Philosophy of Science 56, 130-157.
    • (1989) Philosophy of Science , vol.56 , pp. 130-157
    • Schroeder-Heister, P.1    Schaefer, F.2
  • 43
    • 85012759823 scopus 로고
    • Nonstandard models and related developments
    • L. Harrington et al. (eds), North-Holland, Amsterdam
    • Smoryński, C.: 1985b, 'Nonstandard Models and Related Developments', in L. Harrington et al. (eds), Harvey Friedman's Research on the Foundations of Mathematics, North-Holland, Amsterdam.
    • (1985) Harvey Friedman's Research on the Foundations of Mathematics
    • Smoryński, C.1
  • 44
    • 51249190137 scopus 로고
    • Provability interpretations of modal logic
    • Solovay, R. M.: 1976, 'Provability Interpretations of Modal Logic', Israel Journal of Mathematics 25, 287-304.
    • (1976) Israel Journal of Mathematics , vol.25 , pp. 287-304
    • Solovay, R.M.1
  • 46
    • 26944470573 scopus 로고
    • Interpretability of elementary theories
    • R. Butts and J. Hintikka (eds), Reidel, Dordrecht
    • Szczerba, L.: 1977, 'Interpretability of Elementary Theories', in R. Butts and J. Hintikka (eds), Logic, Foundations of Mathematics and Computing Theory, Reidel, Dordrecht, pp. 129-145.
    • (1977) Logic, Foundations of Mathematics and Computing Theory , pp. 129-145
    • Szczerba, L.1
  • 50
    • 0040325710 scopus 로고
    • Interpretability logic
    • P. P. Petkov (ed.), Plenum Press, New York
    • Visser, A.: 1990, 'Interpretability Logic', in P. P. Petkov (ed.), Mathematical Logic, Plenum Press, New York, pp. 175-208.
    • (1990) Mathematical Logic , pp. 175-208
    • Visser, A.1
  • 52
    • 84972575699 scopus 로고    scopus 로고
    • On the proofs of arithmetical completeness for interpretability logic
    • Zambella, D.: 'On the Proofs of Arithmetical Completeness for Interpretability Logic', Notre Dame Journal of Formal Logic 33, 542-551.
    • Notre Dame Journal of Formal Logic , vol.33 , pp. 542-551
    • Zambella, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.