Homomorphisms and chains of Kripke models

  • Authors:

  • Morteza Moniri;Mostafa Zaare

  • Affiliations:

  • Department of Mathematics, Shahid Beheshti University, G.C., Evin, Tehran, Iran;School of Mathematics and Computer Science, Damghan University, Damghan, Iran

  • Venue:
  • Archive for Mathematical Logic
  • Year:
  • 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.