Intuitionistic validity in T-normal Kripke structures

Annals of Pure and Applied Logic 59 (3):159-173 (1993)
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Abstract

Let T be a first-order theory. A T-normal Kripke structure is one in which every world is a classical model of T. This paper gives a characterization of the intuitionistic theory T of sentences intuitionistically valid in all T-normal Kripke structures and proves the corresponding soundness and completeness theorems. For Peano arithmetic , the theory PA is a proper subtheory of Heyting arithmetic , so HA is complete but not sound for PA-normal Kripke structures

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Citations of this work

Finite sets and infinite sets in weak intuitionistic arithmetic.Takako Nemoto - 2020 - Archive for Mathematical Logic 59 (5-6):607-657.
Intermediate Logics and the de Jongh Property.Dick de Jongh, Rineke Verbrugge & Albert Visser - 2011 - Archive for Mathematical Logic 50 (1-2):197-213.
Classical and Intuitionistic Models of Arithmetic.Kai F. Wehmeier - 1996 - Notre Dame Journal of Formal Logic 37 (3):452-461.
Submodels of Kripke Models.Albert Visser - 2001 - Archive for Mathematical Logic 40 (4):277-295.

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References found in this work

Finite Kripke Models of HA Are Locally PA.E. C. W. Krabbe - 1986 - Notre Dame Journal of Formal Logic 27:528-532.

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