Extendible formulas in two variables in intuitionistic logic
type: Item
instance of: scholarly article
title: Extendible formulas in two variables in intuitionistic logic
zbMATH Open document ID: 1256.03019
author: Nick Bezhanishvili
author: Dick H. J. de Jongh
published in: Studia Logica
publication date: 2012-10-01T00:00:00Z
review text: The paper presents alternative characterizations of exactly provable, extendible and projective formulas in intuitionistic propositional calculus (IPC) using \(n\)-universal models and definable \(p\)-morphisms between them. The notions of exactly provable formulas (also known as exact formulas) of extendible formulas and of projective formulas were introduced respectively by the second author in [Stud. Logic Found. Math. 110, 51--64 (1982; Zbl 0547.03037)], by the second author and \textit{A. Visser} in [in: Logic: from foundations to applications. European logic colloquium, Keele, UK, 1993. Oxford: Clarendon Press. 187--213 (1996; Zbl 0857.03041)] and by \textit{S. Ghilardi} in [J. Symb. Log. 64, No. 2, 859--880 (1999; Zbl 0930.03009)]. For an overview on \(n\)-universal models of IPC see [\textit{A. Chagrov} and \textit{M. Zakharyaschev}, Modal logic. Oxford: Clarendon Press (1997; Zbl 0871.03007)]. From the new characterizations above, the authors give an alternative proof of the fact that every exact formula is extendible; every projective formula is exact and extendible; and they obtain an alternative proof of Ghilardi's theorem (for the restricted case of formulas in two variables) -- every extendible formula is projective. Moreover, a new syntactic description of all (infinitely many) extendible formulas of IPC in two variables is derived.
reviewed by: Gilda Ferreira
Mathematics Subject Classification ID: 03B20
zbMATH DE Number: 6088854
zbMATH Keywords: intuitionistic logic
zbMATH Keywords: universal models
zbMATH Keywords: exact formulas
zbMATH Keywords: extendible formulas
zbMATH Keywords: projective formulas
MaRDI profile type: Publication
full work available at URL: s11225-012-9389-8
OpenAlex ID: W2101864442
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DOI: 10.1007/S11225-012-9389-8
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description: scientific article; zbMATH DE number 6088854