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A Simple Proof of Arithmetical Completeness for $\Pi_1$ -Conservativity Logic
Notre Dame Journal of Formal Logic 35 (3):346-354 (1994)
Abstract
Hájek and Montagna proved that the modal propositional logic ILM is the logic of -conservativity over sound theories containing I (PA with induction restricted to formulas). I give a simpler proof of the same factLinks
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Citations of this work
Transductions in arithmetic.Albert Visser - 2016 - Annals of Pure and Applied Logic 167 (3):211-234.
On the limit existence principles in elementary arithmetic and Σ n 0 -consequences of theories.Lev D. Beklemishev & Albert Visser - 2005 - Annals of Pure and Applied Logic 136 (1-2):56-74.
Hierarchical Incompleteness Results for Arithmetically Definable Extensions of Fragments of Arithmetic.Rasmus Blanck - 2021 - Review of Symbolic Logic 14 (3):624-644.
References found in this work
Provability Interpretations of Modal Logic.Robert M. Solovay - 1981 - Journal of Symbolic Logic 46 (3):661-662.
The interpretability logic of peano arithmetic.Alessandro Berarducci - 1990 - Journal of Symbolic Logic 55 (3):1059-1089.
Provability logics for relative interpretability.Frank Veltman & Dick De Jongh - 1990 - In Petio Petrov Petkov (ed.), Mathematical Logic. Proceedings of the Heyting '88 Summer School. Springer. pp. 31-42.
The logic of π1-conservativity.Petr Hajek & Franco Montagna - 1990 - Archive for Mathematical Logic 30 (2):113-123.
On the proofs of arithmetical completeness for interpretability logic.Domenico Zambella - 1992 - Notre Dame Journal of Formal Logic 33 (4):542-551.
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