Homomorphisms and chains of Kripke models
type: Item
instance of: scholarly article
title: Homomorphisms and chains of Kripke models
zbMATH Open document ID: 1239.03005
author: Morteza Moniri
author: Mostafa Zaare
published in: Archive for Mathematical Logic
publication date: 2011-05-11T00:00:00Z
review text: This paper is a continuation of the study of preservation theorems in intuitionistic logic by the authors [``Preservation theorems for Kripke models'', Math. Log. Q. 55, No. 2, 177--184 (2009; Zbl 1160.03018)]. It is based on Kripke semantics and restricts to those Kripke models defined on a fixed frame \(F\). A homomorphism (resp. embedding) between two Kripke models is a compatible family of maps between the corresponding nodes which preserves atomic formulas from left to right (resp. from both sides). Two classes of formulas \(\mathcal U(\Phi,\Psi)\) and \(\mathcal E(\Phi,\Psi)\) are introduced which extend the ordinary classes of universal and existential formulas. Theories axiomatized by sentences from each one are characterized in terms of homomorphisms and embeddings, similar to the classical cases. Also, a class of theories preserved under the union of chain is introduced. Finally, as an application to intuitionistic arithmetic, an independence result of Wehmeier is strengthened.
reviewed by: Seyed Mohammad Bagheri
Mathematics Subject Classification ID: 03B20
Mathematics Subject Classification ID: 03C40
Mathematics Subject Classification ID: 03C90
Mathematics Subject Classification ID: 03F30
zbMATH DE Number: 5886781
zbMATH Keywords: Kripke model
zbMATH Keywords: intuitionistic logic
zbMATH Keywords: elementary submodel
zbMATH Keywords: universal sentence
zbMATH Keywords: existential sentence
zbMATH Keywords: union of chain
MaRDI profile type: Publication
full work available at URL: s00153-010-0224-5
OpenAlex ID: W2061881968
cites work: Intuitionistic validity in \(T\)-normal Kripke structures
cites work: Some results on Kripke models over an arbitrary fixed frame
cites work: Computer science logic. 10th international workshop, CSL '96. Annual conference of the EACSL, Utrecht, the Netherlands. September 21--27, 1996. Selected papers
cites work: Kripke submodels and universal sentences
cites work: Syntactic preservation theorems for intuitionistic predicate logic
cites work: Q4336034
cites work: On the structure of kripke models of heyting arithmetic
cites work: Preservation theorems for Kripke models
cites work: Existence and feasibility in arithmetic
cites work: Constructivism in mathematics. An introduction. Volume II
cites work: Submodels of Kripke models
cites work: Fragments of HA based on \(\Sigma_ 1\)-induction
DOI: 10.1007/S00153-010-0224-5
description: scientific article; zbMATH DE number 5886781