Krivine's intuitionistic proof of classical completeness (for countable languages)
type: Item
instance of: scholarly article
title: Krivine's intuitionistic proof of classical completeness (for countable languages)
zbMATH Open document ID: 1062.03058
author: Stefano Berardi
author: Silvio Valentini
published in: Annals of Pure and Applied Logic
publication date: 2004-11-22T00:00:00Z
review text: The first part of the paper presents Krivine's intuitionistic version of Gödel's completeness theorem for first-order classical predicate logic [see \textit{J. L. Krivine}, Bull. Symb. Log. 2, 405--421 (1996; Zbl 0872.03004)]. The second part makes use of the ideas of Krivine's proof to derive intuitionistically some suitable variants of the two following classical theorems: the Ultrafilter Theorem for countable Boolean algebras and the Maximal Ideal Theorem for countable rings.
Mathematics Subject Classification ID: 03F55
Mathematics Subject Classification ID: 03C07
Mathematics Subject Classification ID: 03B10
zbMATH DE Number: 2117326
zbMATH Keywords: first-order classical logic
zbMATH Keywords: Gödel's completeness theorem
zbMATH Keywords: intuitionistic completeness
zbMATH Keywords: ultrafilter theorem
zbMATH Keywords: maximal ideal theorem
reviewed by: Victor N. Krivtsov
MaRDI profile type: Publication
full work available at URL: j.apal.2004.01.002
OpenAlex ID: W2073185604
cites work: Intuitionistic completeness for first order classical logic
cites work: Une Preuve Formelle et Intuitionniste du Théorème de Complétude de la Logique Classique
cites work: Undecidability and intuitionistic incompleteness
cites work: Q5537599
DOI: 10.1016/J.APAL.2004.01.002
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description: scientific article; zbMATH DE number 2117326