On the predicate logics of finite Kripke frames
type: Item
instance of: scholarly article
title: On the predicate logics of finite Kripke frames
zbMATH Open document ID: 0839.03011
DOI: 10.1007/BF01058533
published in: Studia Logica
publication date: 1995-02-22T00:00:00Z
review text: The intermediate predicate logic characterized by the class of all finite Kripke frames (Lfin) is studied. Beforehand by the same author, it is proved that Lfin is not recursively axiomatizable, but that Lfin is \(\Pi^0_2\)-arithmetical. On the other hand, Lfin can be expressed as the intersection of the logics \(\text{LB}_n \text{P}^+_m\), which are characterized by all posets of finite height \(\leq m\) and finite branching \(\leq n\), and which are obviously finitely axiomatizable. Further, the logic \(\text{LP}^+_m\), which is characterized by all posets of height \(\leq m\), is known to be finitely axiomatizable. In this paper, it is proved that \(\text{LB}_n \text{P}^+_m= (\text{LP}^+_m+ \text{B}_n)\), where \(\text{B}_n\) is the propositional axioms of branching \(\leq n\).
Mathematics Subject Classification ID: 03B55
zbMATH DE Number: 724130
zbMATH Keywords: intermediate predicate logic
zbMATH Keywords: finite Kripke frames
zbMATH Keywords: posets
zbMATH Keywords: finitely axiomatizable
author: Dmitrij Skvortsov
reviewed by: Tsutomu Hosoi
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01058533
OpenAlex ID: W2019451333
description: scientific article; zbMATH DE number 724130