Interpreting reflexive theories in finitely many axioms
Fundamenta Mathematicae (1997)
- Volume: 152, Issue: 2, page 99-116
- ISSN: 0016-2736
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top- [1] A. Berarducci and P. D’Aquino, -complexity of the relation , Ann. Pure Appl. Logic 75 (1995), 49-56.
- [2] A. Berarducci and R. Verbrugge, On the provability logic of bounded arithmetic, ibid. 61 (1993), 75-93. Zbl0803.03037
- [3] B S. R. Buss, Bounded Arithmetic, Bibliopolis, Napoli, 1986.
- [4] D P. D’Aquino, A sharpened version of McAloon’s theorem on initial segments of models of , Ann. Pure Appl. Logic 61 (1993), 49-62.
- [5] P. Hájek and P. Pudlák, Metamathematics of First-Order Arithmetic, Springer, Berlin, 1993. Zbl0781.03047
- [6] J R. G. Jeroslow, Non-effectiveness in S. Orey's arithmetical compactness theorem, Z. Math. Logic Grundlangen Math. 17 (1971), 285-289. Zbl0234.02036
- [7] P. Lindström, Some results on interpretability, in: Proc. 5th Scandinavian Logic Sympos., F. V. Jensen, B. H. Mayoh and K. K. Møller (eds.), Aalborg Univ. Press, 1979, 329-361.
- [8] P. Lindström, On partially conservative sentences and interpretability, Proc. Amer. Math. Soc. 91 (1984), 436-443. Zbl0577.03028
- [9] J. Paris and A. Wilkie, Counting sets, Fund. Math. 127 (1986), 67-76. Zbl0627.03018
- [10] J. B. Paris, A. J. Wilkie and A. R. Woods, Provability of the pigeonhole principle and the existence of infinitely many primes, J. Symbolic Logic 53 (1988), 1235-1244. Zbl0688.03042
- [11] P. Pudlák, Cuts, consistency statements and interpretations, J. Symbolic Logic 50 (1985), 423-441. Zbl0569.03024
- [12] P. Pudlák, On the length of proofs of finitistic consistency statements in first order theories, in: Logic Colloquium '84, J. B. Paris, A. J. Wilkie and G. M. Wilmers (eds.), North-Holland, Amsterdam, 1986, 165-196.
- [13] W. Sieg, Fragments of arithmetic, Ann. Pure Appl. Logic 28 (1985), 33-71. Zbl0558.03029
- [14] C. Smoryński, Nonstandard models and related developments, in: Harvey Friedman's Research on the Foundations of Mathematics, L. A. Harrington, M. D. Morley, A. Ščedrov and S. G. Simpson (eds.), North-Holland, Amsterdam, 1985, 179-229.
- [15] V. Švejdar, A sentence that is difficult to interpret, Comment. Math. Univ. Carolin 22 (1981), 661-666. Zbl0484.03032
- [16] A. Visser, Interpretability logic, in: Mathematical Logic, P. P. Petkov (ed.), Plenum Press, New York, 1990, 175-209. Zbl0793.03064
- [17] A. Visser, An inside view of EXP; or, the closed fragment of the provability logic of with a propositional constant for EXP, J. Symbolic Logic 57 (1992), 131-165. Zbl0785.03008
- [18] A. Visser, The unprovability of small inconsistency, A study of local and global interpretability, Arch. Math. Logic 32 (1993), 275-298. Zbl0795.03080
- [19] W A. J. Wilkie, On sentences interpretable in systems of arithmetic, in: Logic Colloquium '84, J. B. Paris, A. J. Wilkie and G. M. Wilmers (eds.), North-Holland, Amsterdam, 1986, 329-342.
- [20] A. J. Wilkie and J. B. Paris, On the scheme of induction for bounded arithmetic formulas, Ann. Pure Appl. Logic 35 (1987), 261-302. Zbl0647.03046