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## Fundamenta Mathematicae

1997 | 152 | 2 | 99-116
Tytuł artykułu

### Interpreting reflexive theories in finitely many axioms

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
For finitely axiomatized sequential theories F and reflexive theories R, we give a characterization of the relation 'F interprets R' in terms of provability of restricted consistency statements on cuts. This characterization is used in a proof that the set of $∏_1$ (as well as $∑_1$) sentences π such that GB interprets ZF+π is $Σ^0_3$-complete.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
99-116
Opis fizyczny
Daty
wydano
1997
otrzymano
1995-08-15
poprawiono
1996-10-22
Twórcy
autor
• Department of Philosophy, Utrecht University, Heidelberglaan 8, 3584 CS Utrecht, The Netherlands
Bibliografia
• [1] A. Berarducci and P. D'Aquino, $Δ_0$-complexity of the relation $y = ∏_i ≤ nF(i)$, 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.
• [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 $IΔ_0$, Ann. Pure Appl. Logic 61 (1993), 49-62.
• [5] P. Hájek and P. Pudlák, Metamathematics of First-Order Arithmetic, Springer, Berlin, 1993.
• [6] J R. G. Jeroslow, Non-effectiveness in S. Orey's arithmetical compactness theorem, Z. Math. Logic Grundlangen Math. 17 (1971), 285-289.
• [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.
• [9] J. Paris and A. Wilkie, Counting $Δ_0$ sets, Fund. Math. 127 (1986), 67-76.
• [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.
• [11] P. Pudlák, Cuts, consistency statements and interpretations, J. Symbolic Logic 50 (1985), 423-441.
• [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.
• [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.
• [16] A. Visser, Interpretability logic, in: Mathematical Logic, P. P. Petkov (ed.), Plenum Press, New York, 1990, 175-209.
• [17] A. Visser, An inside view of EXP; or, the closed fragment of the provability logic of $IΔ_0+Ω_1$ with a propositional constant for EXP, J. Symbolic Logic 57 (1992), 131-165.
• [18] A. Visser, The unprovability of small inconsistency, A study of local and global interpretability, Arch. Math. Logic 32 (1993), 275-298.
• [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.
Typ dokumentu
Bibliografia
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