Intuitionistic axiomatizations for bounded extension Kripke models

Annals of Pure and Applied Logic 124 (1-3):267-285 (2003)
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Abstract

We present axiom systems, and provide soundness and strong completeness theorems, for classes of Kripke models with restricted extension rules among the node structures of the model. As examples we present an axiom system for the class of cofinal extension Kripke models, and an axiom system for the class of end-extension Kripke models. We also show that Heyting arithmetic is strongly complete for its class of end-extension models. Cofinal extension models of HA are models of Peano arithmetic

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Saeed Salehi
University of Tabriz

References found in this work

A logic stronger than intuitionism.Sabine Görnemann - 1971 - Journal of Symbolic Logic 36 (2):249-261.
Models of Peano Arithmetic.Richard Kaye - 1991 - Clarendon Press.
Intuitionistic validity in T-normal Kripke structures.Samuel R. Buss - 1993 - Annals of Pure and Applied Logic 59 (3):159-173.
Classical and Intuitionistic Models of Arithmetic.Kai F. Wehmeier - 1996 - Notre Dame Journal of Formal Logic 37 (3):452-461.

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