Quantifier elimination for a class of intuitionistic theories
type: Item
instance of: scholarly article
title: Quantifier elimination for a class of intuitionistic theories
zbMATH Open document ID: 1159.03021
DOI: 10.1215/00294527-2008-012
author: Ben Ellison
author: Jonathan Fleischmann
author: Dan McGinn
author: Wim Ruitenburg
published in: Notre Dame Journal of Formal Logic
publication date: 2008-10-20T00:00:00Z
review text: It has often been assumed that intuitionistic theories admitting quantifier elimination are `nearly classical' since Smoryński and Bagheri studied the problem focusing on such theories. In this paper, however, `very intuitionistic' theories are constructed so as to admit quantifier elimination by extending the former work of one of the authors, Ruitenburg. In the classical case, certain theories over finite relational languages, called JRS theories here after Jaskowski, Rabin, and Scott, are known to admit quantifier elimination. So, given a classical JRS theory, the authors construct a Kripke model by featuring that a JRS theory is Fraïssé-homogeneous and countably categorical. The intuitionistic theories determined by Kripke models thus constructed are, in fact, shown to admit quantifier elimination as well as to be complete including negations of some classical tautologies. Thus the theories enjoy several interesting characteristics, among which their intuitionistic universal fragments are investigated in particular. For example, the axioms to determine them are given explicitly.
reviewed by: Osamu Sonobe
Mathematics Subject Classification ID: 03C10
Mathematics Subject Classification ID: 03C35
Mathematics Subject Classification ID: 03C90
Mathematics Subject Classification ID: 03F55
zbMATH DE Number: 5353774
zbMATH Keywords: quantifier elimination
zbMATH Keywords: intuitionistic theory
zbMATH Keywords: Kripke model
zbMATH Keywords: Fraïssé-homogeneous
zbMATH Keywords: countably categorical
zbMATH Keywords: intuitionistic universal fragment
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/00294527-2008-012
OpenAlex ID: W2141172560
description: scientific article; zbMATH DE number 5353774