Undecidability of Brouwerian semilattices
type: Item
instance of: scholarly article
title: Undecidability of Brouwerian semilattices
zbMATH Open document ID: 0616.03024
DOI: 10.1007/BF01224033
author: Katarzyna Idziak
published in: Algebra Universalis
publication date: 1986-01-01T00:00:00Z
review text: The author shows that the first order theory of finite Brouwerian semilattices of the variety generated by the algebra \(2^ 2\oplus 1\) is undecidable. She proves the theorem by interpreting finite graphs into finite Brouwerian semilattices from the variety. The result gives an example of a finitely generated arithmetical variety whose finite members have an undecidable first order theory. This answers in negative a question of \textit{S. Burris} and \textit{H. P. Sankappanavar} [A course of universal algebra (1981; Zbl 0478.08001)].
Mathematics Subject Classification ID: 03D35
Mathematics Subject Classification ID: 08B99
zbMATH DE Number: 3997773
zbMATH Keywords: first order theory
zbMATH Keywords: finite Brouwerian semilattices
zbMATH Keywords: finite graphs
zbMATH Keywords: finitely generated arithmetical variety
reviewed by: Oleg Belegradek
MaRDI profile type: Publication
cites work: Q3934450
cites work: Q5509710
cites work: Algebras Whose Congruence Lattices are Distributive.
cites work: Q5586299
description: scientific article; zbMATH DE number 3997773