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Interpretability in PRA

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    0332835 - ÚI 2010 RIV NL eng J - Journal Article
    Bílková, Marta - De Jongh, D. - Joosten, J.J.
    Interpretability in PRA.
    [Interpretovatelnost v PRA.]
    Annals of Pure and Applied Logic. Roč. 161, č. 2 (2009), s. 128-138. ISSN 0168-0072. E-ISSN 1873-2461
    R&D Projects: GA AV ČR IAA900090703
    Grant - others:GA ČR(CZ) GA401/06/0387
    Institutional research plan: CEZ:AV0Z10300504
    Keywords : interpretability * arithmetic * primitive recursive arithmetic * interpretability logic
    Subject RIV: BA - General Mathematics
    Impact factor: 0.667, year: 2009

    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.

    Článek se zabývá logikou interpretovatelnosti aritmetické teorie PRA. Protože PRA není ani podstatně reflexivní ani konečně axiomatizovatelná, známé výsledky aritmetické úplnosti nelze použít: IL(PRA) není ani ILM, ani ILP. Ukážeme důsledky dvou aritmetických principů - tzv. Beklemiševova principu B a Zambellova principu Z - pro modální logiku IL(PRA). Nalezneme podmínku definovanou na rámcích principem B a ukážeme, že Z plyne z omezené varianty principu B. Nakonec shrneme známé souvislosti IL(PRA) s jinými důležitými principy interpretovatelnosti.
    Permanent Link: http://hdl.handle.net/11104/0177966

     
     
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