Decidability of the elementary theory of universal semifields of the second kind
type: Item
instance of: scholarly article
title: Decidability of the elementary theory of universal semifields of the second kind
zbMATH Open document ID: 0626.06019
DOI: 10.1007/BF00969270
author: R. Gulamov
published in: Siberian Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: A universal semifield \(S_{\nabla}\) in the sense of \textit{M. Ya. Antonovskij}, \textit{V. G. Boltyanskij} and \textit{T. A. Sarymsakov} [Topological Boolean Algebras (Tashkent 1963; Zbl 0154.012)] is called a semifield of the second kind (or continuous) if the Boolean algebra \(\nabla\) is atom-free. Using a result of \textit{A. Macintyre} [Fundam. Math. 81, 73-89 (1973; Zbl 0317.02065)] the author proves that the theory of universal semifields of the second kind is decidable. He gives a system of axioms for such semifields.
Mathematics Subject Classification ID: 06F25
Mathematics Subject Classification ID: 03C35
Mathematics Subject Classification ID: 12J17
Mathematics Subject Classification ID: 16W80
zbMATH DE Number: 4016979
zbMATH Keywords: decidability
zbMATH Keywords: completeness
zbMATH Keywords: real-closed commutative regular f-rings
zbMATH Keywords: Boolean algebra
zbMATH Keywords: universal semifields of the second kind
zbMATH Keywords: system of axioms
MaRDI profile type: Publication
cites work: Model-completeness for sheaves of structures
cites work: Q3283133
cites work: Q5605672
cites work: Q3958432
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description: scientific article; zbMATH DE number 4016979