Archive for Mathematical Logic 50 (3-4):431-443 (2011)

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Abstract
In this paper we define a suitable version of the notion of homomorphism for Kripke models of intuitionistic first-order logic and characterize theories that are preserved under images and also those that are preserved under inverse images of homomorphisms. Moreover, we define a notion of union of chain for Kripke models and define a class of formulas that is preserved in unions of chains. We also define similar classes of formulas and investigate their behavior in Kripke models. An application to intuitionistic first-order arithmetic is also given
Keywords Kripke model  Intuitionistic logic  Submodel  Elementary submodel  Universal sentence  Existential sentence  Union of chain
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DOI 10.1007/s00153-010-0224-5
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References found in this work BETA

A Shorter Model Theory.Wilfrid Hodges - 2000 - Studia Logica 64 (1):133-134.
Existence and Feasibility in Arithmetic.Rohit Parikh - 1971 - Journal of Symbolic Logic 36 (3):494-508.
Fragments of $HA$ Based on $\Sigma_1$ -Induction.Kai F. Wehmeier - 1997 - Archive for Mathematical Logic 37 (1):37-49.
Intuitionistic Validity in T-Normal Kripke Structures.Samuel R. Buss - 1993 - Annals of Pure and Applied Logic 59 (3):159-173.
Submodels of Kripke Models.Albert Visser - 2001 - Archive for Mathematical Logic 40 (4):277-295.

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