Finite axiomatizations for existentially closed posets and semilattices
type: Item
instance of: scholarly article
title: Finite axiomatizations for existentially closed posets and semilattices
zbMATH Open document ID: 0611.03013
DOI: 10.1007/BF00390107
published in: Order
publication date: 1986-01-01T00:00:00Z
review text: It is well known that any universal first order relational theory K with the joint embedding and the amalgamation property admits an \(\aleph_ 0\)-categorical model-completion \(\bar K\) which is given by formalizing the finite diagrams of models of K according to the back and forth method [e.g. the reviewer's dissertation, Z. Math. Logik Grundlagen Math. 15, 37-48 (1969; Zbl 0188.321), p. 42, footnote]. Applied to totally ordered sets the method yields the densely ordered sets without endpoints. The authors establish similar finite axiomatizations of \(\bar K\) for posets and semilattices.
Mathematics Subject Classification ID: 03C35
Mathematics Subject Classification ID: 06A06
Mathematics Subject Classification ID: 06A12
Mathematics Subject Classification ID: 06A05
Mathematics Subject Classification ID: 03C60
zbMATH DE Number: 3987258
zbMATH Keywords: existentially closed posets
zbMATH Keywords: existentially closed semilattices
zbMATH Keywords: finite axiomatizability
zbMATH Keywords: model companions
zbMATH Keywords: categoricity
author: Michael Albert
author: Stanley N. Burris
reviewed by: Klaus Kaiser
MaRDI profile type: Publication
cites work: Model companions for finitely generated universal Horn classes
cites work: Sheaf Constructions and Their Elementary Properties
cites work: Q4056178
cites work: Q3037400
cites work: Existentially closed structures
cites work: A note on ℵ0-categorical model-companions
full work available at URL: https://doi.org/10.1007/bf00390107
OpenAlex ID: W2048036952
description: scientific article; zbMATH DE number 3987258