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TWO NEW SERIES OF PRINCIPLES IN THE INTERPRETABILITY LOGIC OF ALL REASONABLE ARITHMETICAL THEORIES

Published online by Cambridge University Press:  12 December 2019

EVAN GORIS
Affiliation:
INDEPENDENT SCHOLAR E-mail: evan.goris@xillio.com
JOOST J. JOOSTEN
Affiliation:
DEPARTMENT OF PHILOSOPHY UNIVERSITY OF BARCELONA C. MONTALEGRE 6 08001 BARCELONA CATALONIA, SPAIN E-mail: jjoosten@ub.eduURL: http://www.phil.uu.nl/~jjoosten/
Corresponding

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 article 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.

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Articles
Copyright
Copyright © The Association for Symbolic Logic 2019 

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TWO NEW SERIES OF PRINCIPLES IN THE INTERPRETABILITY LOGIC OF ALL REASONABLE ARITHMETICAL THEORIES
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