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Title of article :
Interpretability in
Author/Authors :
Bيlkovل، نويسنده , , Marta and de Jongh، نويسنده , , Dick and Joosten، نويسنده , , Joost J.، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2009
Pages :
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Abstract :
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 IL M or IL P . IL ( PRA ) does, of course, contain all the principles known to be part of IL (All), the interpretability logic of the principles common to all reasonable arithmetical theories. In this paper, we take 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 , neither of which is a part of IL (All). Both principles and their interrelation are submitted to a modal study. In particular, we prove a frame condition for B . Moreover, we prove that Z follows from a restricted form of B . Finally, we give an overview of the known relationships of IL ( PRA ) to important other interpretability principles.
Keywords :
Interpretability , Primitive recursive arithmetic , arithmetic , Interpretability logic
Journal title :
Annals of Pure and Applied Logic
Journal title :
Annals of Pure and Applied Logic
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