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NON–WELL-FOUNDED DERIVATIONS IN THE GÖDEL-LÖB PROVABILITY LOGIC

Published online by Cambridge University Press:  26 November 2019

DANIYAR SHAMKANOV
DANIYAR SHAMKANOV*
Affiliation:
Steklov Mathematical Institute of Russian Academy of Sciences and National Research University Higher School of Economics
*
*STEKLOV MATHEMATICAL INSTITUTE OF RUSSIAN ACADEMY OF SCIENCES GUBKINA STR. 8, 119991, MOSCOW, RUSSIA and NATIONAL RESEARCH UNIVERSITY HIGHER SCHOOL OF ECONOMICS FACULTY OF MATHEMATICS USACHEVA STR. 6, 119048, MOSCOW, RUSSIA E-mail: [email protected]
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Abstract

We consider Hilbert-style non–well-founded derivations in the Gödel-Löb provability logic GL and establish that GL with the obtained derivability relation is globally complete for algebraic and neighbourhood semantics.

Keywords

03B65provability logicalgebraic semanticsneighbourhood semanticsscattered topological spacesglobal consequence relationsnon–well-founded derivations
Type
Research Article
Information
The Review of Symbolic Logic , Volume 13 , Issue 4 , December 2020 , pp. 776 - 796
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Copyright
Copyright © Association for Symbolic Logic 2019 

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