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The Journal of Symbolic Logic The Journal of Symbolic Logic

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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  and
JOOST J. JOOSTEN
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
E-mail address:
evan.goris@xillio.com
jjoosten@ub.edu
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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.

Keywords

03B45 03B60 03F30 03F40 03F45 interpretability logics interpretations definable cuts weak arithmetics formal provability
Type
Articles
Information
The Journal of Symbolic Logic , Volume 85 , Issue 1 , March 2020 , pp. 1 - 25
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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