Interpolation property and superintuitionistic predicate logics
type: Item
instance of: scholarly article
title: Interpolation property and superintuitionistic predicate logics
zbMATH Open document ID: 0914.03029
author: D. E. Tishkovskij
published in: Siberian Mathematical Journal
publication date: 1999-05-11T00:00:00Z
review text: The article deals with the interpolation problem for extensions of the first-order predicate logic. For propositional superintuitionistic logics, this problem was completely solved by \textit{L. L. Maksimova} [Algebra Logika 16, No. 6, 643-681 (1977; Zbl 0403.03047)]. The author formulates a sufficient condition that makes it possible to refute the interpolation theorem. The condition is based on an interesting explicit construction of counterexamples to the interpolation property. On the basis of this condition, it is proven that the interpolation theorem fails for a wide natural class of predicate superintuitionistic logics. Namely, for logics characterized by classes of Kripke frames such that the cardinality of all or almost all domains equals a given fixed natural \(i>2\). In particular, the interpolation property is refuted for predicate extensions of propositional logics with interpolation property. The article also contains a series of examples of superintuitionistic predicate logics with equality such that these logics possess the interpolation property whereas their pure fragments (without equality) do not possess this property.
Mathematics Subject Classification ID: 03B55
Mathematics Subject Classification ID: 03B60
zbMATH DE Number: 1286429
zbMATH Keywords: superintuitionistic predicate logic
zbMATH Keywords: interpolation property
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1286429