Existentially closed semilattices
type: Item
instance of: scholarly article
title: Existentially closed semilattices
zbMATH Open document ID: 0604.06004
DOI: 10.1007/BF01188050
author: Volker Weispfenning
published in: Algebra Universalis
publication date: 1985-01-01T00:00:00Z
review text: An algebra A is algebraically closed (existentially closed) in a class K of algebras, if every finite system of equations (and inequalities) with constants from A which is solvable in a K-extension of A already has a solution in A. In the paper under review these properties are investigated for the class BSL of bounded semilattices. In the first part it is shown that BSL has the strong amalgamation property: it follows from an earlier theorem by the author [Arch. Math. Logik Grundlagenforsch. 19, 23-29 (1978; Zbl 0408.03024)] that the class BSL of existentially closed bounded semilattices is the model completion of BSL and that it is \(\aleph_ 0\)-categorical. In the second part, an axiomatic description of BSL' and the class BSL'' of algebraically closed bounded semilattices is given; furthermore, some basic properties of these classes and some connections among these and related classes of lattices are exhibited. Throughout the article, a fruitful mixture of algebraic and model theoretic techniques is employed.
Mathematics Subject Classification ID: 06A12
Mathematics Subject Classification ID: 03C60
Mathematics Subject Classification ID: 06B20
zbMATH DE Number: 3974999
zbMATH Keywords: finite system of equations
zbMATH Keywords: strong amalgamation property
zbMATH Keywords: existentially closed bounded semilattices
zbMATH Keywords: model completion
zbMATH Keywords: algebraically closed bounded semilattices
MaRDI profile type: Publication
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cites work: Complexity of Boolean algebras
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cites work: A note on ℵ0-categorical model-companions
cites work: Q3758805
description: scientific article; zbMATH DE number 3974999