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Title: Two new series of principles in the interpretability logic of all reasonable arithmetical theories
Author: Goris, Evan
Joosten, Joost J.
Keywords: Lògica matemàtica
Mathematical logic
Issue Date: Mar-2020
Publisher: Association for Symbolic Logic.
Abstract: The provability logic of a theory T captures the structural behavior of formalized provability in T as provable in T itself. Like provability, one can formalize the notion of relative interpretability giving rise to interpretability logics. Where provability logics are the same for all moderately sound theories of some minimal strength, interpretability logics do show variations. The logic IL(All) is defined as the collection of modal principles that are provable in any moderately sound theory of some minimal strength. In this paper we raise the previously known lower bound of IL(All) by exhibiting two series of principles which are shown to be provable in any such theory. Moreover, we compute the collection of frame conditions for both series.
Note: Versió postprint del document publicat a:
It is part of: Journal of Symbolic Logic, 2020, vol. 85, num. 1, p. 1-25
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ISSN: 0022-4812
Appears in Collections:Articles publicats en revistes (Filosofia)

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