On classes of arithmetical counterparts of modal provability logics
type: Item
instance of: scholarly article
title: On classes of arithmetical counterparts of modal provability logics
zbMATH Open document ID: 0711.03002
author: E. Yu. Nogina
published in: Moscow University Mathematics Bulletin
publication date: 1990-01-01T00:00:00Z
review text: A logic of provability \(\ell\) is defined as a modal logic which describes those principles of provability in Peano Arithmetic PA that can be demonstrated by means of a given theory T extending PA. In this situation T is called a counterpart of \(\ell\). Obviously, each logic of provability \(\ell\) has a smallest counterpart. The paper shows that a given logic of provability has a continuum of counterparts, each two of which are inconsistent. As a corollary we see that none of the logics of provability has a largest counterpart.
Mathematics Subject Classification ID: 03B45
Mathematics Subject Classification ID: 03F30
Mathematics Subject Classification ID: 03F40
zbMATH DE Number: 4168651
zbMATH Keywords: provability logic
zbMATH Keywords: modal logic
zbMATH Keywords: principles of provability in Peano Arithmetic
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4168651