The model companion of width-two orders
type: Item
instance of: scholarly article
title: The model companion of width-two orders
zbMATH Open document ID: 0908.03041
DOI: 10.1023/A:1006058625041
author: Anthony Bonato
author: Dejan Delić
published in: Order
publication date: 1999-03-02T00:00:00Z
review text: Let \(W_n\) denote the universal class of all width-\(n\) orders. Building on work of Pouzet the authors prove that the class of existentially closed members of \(W_2\), \(W^{\text{ec}}_2\), is a first-order class. In fact for \(A\in W_2\), \(A\in W^{\text{ec}}_2\) if and only if \(A\) is a linear sum of d-homogeneous width-2 orders. As corollaries of their characterization they have that the model companion of \(W_2\) exists and it is complete, decidable, non-finitely axiomatizable, and has \(2^{\aleph}_0\) countable models. Another corollary is that \(W_2\) has a decidable universal theory.
reviewed by: J. M. Plotkin
Mathematics Subject Classification ID: 03C52
Mathematics Subject Classification ID: 06A06
zbMATH DE Number: 1210095
zbMATH Keywords: model companion
zbMATH Keywords: width-two order
zbMATH Keywords: d-homogeneous order
zbMATH Keywords: existentially closed
MaRDI profile type: Publication
full work available at URL: a:1006058625041
OpenAlex ID: W1554517875
description: scientific article; zbMATH DE number 1210095