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Interpretability in PRA
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SYSNO ASEP 0332835 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Interpretability in PRA Title Interpretovatelnost v PRA Author(s) Bílková, Marta (UIVT-O) SAI, RID, ORCID
De Jongh, D. (NL)
Joosten, J.J. (NL)Source Title Annals of Pure and Applied Logic. - : Elsevier - ISSN 0168-0072
Roč. 161, č. 2 (2009), s. 128-138Number of pages 11 s. Language eng - English Country NL - Netherlands Keywords interpretability ; arithmetic ; primitive recursive arithmetic ; interpretability logic Subject RIV BA - General Mathematics R&D Projects IAA900090703 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR) CEZ AV0Z10300504 - UIVT-O (2005-2011) UT WOS 000271342500003 EID SCOPUS 70349432210 DOI 10.1016/j.apal.2009.05.012 Annotation In this paper we study IL(PRA), the interpretability logic of PRA. As PRA is neither an essentially reflexive theory nor finitely axiomatizable, the two known arithmetical completeness results do not apply to PRA: IL(PRA) is not ILM or ILP. We consider two arithmetical properties of PRA and see what their consequences in the modal logic IL(PRA) are. These properties are reflected in the so-called Beklemishev Principle B, and Zambella's Principle Z. We prove a frame condition for B, and that Z follows from a restricted form of B. Finally, we give an overview of the known relationships of IL(PRA) to important other interpetability principles. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2010
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