Some results on Kripke models over an arbitrary fixed frame

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Mathematical Logic Quarterly 49 (5):479-484 (2003)
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Abstract

We study the relations of being substructure and elementary substructure between Kripke models of intuitionistic predicate logic with the same arbitrary frame. We prove analogues of Tarski's test and Löwenheim-Skolem's theorems as determined by our definitions. The relations between corresponding worlds of two Kripke models [MATHEMATICAL SCRIPT CAPITAL K] ⪯ [MATHEMATICAL SCRIPT CAPITAL K]′ are studied

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10.1002/malq.200310052

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Citations of this work

Syntactic Preservation Theorems for Intuitionistic Predicate Logic.Jonathan Fleischmann - 2010 - Notre Dame Journal of Formal Logic 51 (2):225-245.
Back and Forth Between First-Order Kripke Models.Tomasz Połacik - 2008 - Logic Journal of the IGPL 16 (4):335-355.
Preservation theorems for Kripke models.Morteza Moniri & Mostafa Zaare - 2009 - Mathematical Logic Quarterly 55 (2):177-184.
Homomorphisms and chains of Kripke models.Morteza Moniri & Mostafa Zaare - 2011 - Archive for Mathematical Logic 50 (3-4):431-443.
Some preservation theorems in an intermediate logic.Seyed M. Bagheri - 2006 - Mathematical Logic Quarterly 52 (2):125-133.

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References found in this work

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.
Submodels of Kripke models.Albert Visser - 2001 - Archive for Mathematical Logic 40 (4):277-295.
Model Theory for Intuitionistic Logic.Dov M. Gabbay - 1972 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 18 (4-6):49-54.
Model Theory for Intuitionistic Logic.Dov M. Gabbay - 1972 - Mathematical Logic Quarterly 18 (4‐6):49-54.

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