On the interpretability of arithmetic in temporal logic
type: Item
instance of: scholarly article
title: On the interpretability of arithmetic in temporal logic
zbMATH Open document ID: 0703.03004
DOI: 10.1016/0304-3975(90)90161-A
author: Fred Kröger
published in: Theoretical Computer Science
publication date: 1990-01-01T00:00:00Z
review text: In this paper techniques of extending first-order temporal theories by definitions of new function symbols are developed after the manner of classical first-order logic. These techniques have enabled the author to interpret classical first-order theories, including arithmetic in particular, in a temporal one. The results of \textit{A. Szalas} [Theor. Comput. Sci. 47, 329-334 (1986; Zbl 0622.03012)] are strengthened as follows: There is no sound and complete finitistic axiomatization of first-order temporal logic with equality (with \(\bigcirc\) and \(\square)\) in each of the following two cases: (a) The language allows quantification only over global variables and contains at least two binary function symbols. (b) The language allows quantification over global and local variables and has an arbitrary (particularly empty) signature.
Mathematics Subject Classification ID: 03B45
Mathematics Subject Classification ID: 03B70
Mathematics Subject Classification ID: 68Q55
zbMATH DE Number: 4152341
zbMATH Keywords: extending first-order temporal theories
zbMATH Keywords: arithmetic
reviewed by: Hirokazu Nishimura
MaRDI profile type: Publication
cites work: Model theory
cites work: Q3749040
cites work: Q3785898
cites work: Q3746875
cites work: Q5537599
cites work: Concerning the semantic consequence relation in first-order temporal logic
cites work: Incompleteness of first-order temporal logic with until
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description: scientific article; zbMATH DE number 4152341