Intuitionistic axiomatizations for bounded extension Kripke models.
type: Item
instance of: scholarly article
title: Intuitionistic axiomatizations for bounded extension Kripke models.
zbMATH Open document ID: 1040.03044
DOI: 10.1016/S0168-0072(03)00058-7
author: Mohammad Ardeshir
author: Wim Ruitenburg
author: Saeed Salehi
published in: Annals of Pure and Applied Logic
publication date: 2003-11-25T00:00:00Z
review text: In this paper some particular sets of formulas, or axiom systems, are introduced by means of syntactical closure conditions, and any extension of intuitionistic logic by such an axiom system is proved to be strongly complete with respect to a class of Kripke models defined suitably according to the axiom system. The classes of Kripke models thus characterized cover several interesting special cases such as cofinal extension models, G-expansion models, and end-extension models, where a G-expansion model with the falsehood G, for example, means a constant domain model. As applications, therefore, the authors obtain strongly complete axiomatizations for the extensions of intuitionistic logic characterized by these classes of Kripke models respectively. Moreover, the authors discuss applications to Heyting arithmetic HA as well, among which it is proved, for instance, that HA is strongly complete for its class of end-extension Kripke models, and cofinal extension models of HA are models of Peano arithmetic.
reviewed by: Osamu Sonobe
Mathematics Subject Classification ID: 03F55
Mathematics Subject Classification ID: 03B20
Mathematics Subject Classification ID: 03C62
Mathematics Subject Classification ID: 03C90
Mathematics Subject Classification ID: 03F30
Mathematics Subject Classification ID: 03F50
zbMATH DE Number: 2009289
zbMATH Keywords: strong completeness
zbMATH Keywords: intuitionistic logic
zbMATH Keywords: Kripke model
zbMATH Keywords: Heyting arithmetic
zbMATH Keywords: cofinal extension
zbMATH Keywords: end-extension
zbMATH Keywords: constant domain
Wikidata QID: Q57533073
MaRDI profile type: Publication
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DBLP publication ID: journals/apal/ArdeshirRS03
description: scientific article; zbMATH DE number 2009289