Martin's conjecture for \(\omega\)-stable theories
type: Item
instance of: scholarly article
title: Martin's conjecture for \(\omega\)-stable theories
zbMATH Open document ID: 0595.03029
DOI: 10.1007/BF02760643
author: E. Bouscaren
published in: Israel Journal of Mathematics
publication date: 1984-01-01T00:00:00Z
review text: Suppose T is a complete \(L_{\omega \omega}\)-theory with less than \(2^{\aleph_ 0}\) countable models. It is shown that the \(L_ 1(T)\)- theory of any countable model is \(\aleph_ 0\)-categorical, where \(L_ 1(T)\) denotes the smallest fragment of \(L_{\omega_ 1\omega}\) containing \(L_{\omega \omega}\) and for each \(n\in \omega\), all complete n-types of T. The proof uses the analysis of the models of such a theory given by \textit{S. Shelah}, \textit{L. Harrington}, and \textit{M. Makkai} [Isr. J. Math. 49, 269-280 (1984; Zbl 0584.03021)].
Mathematics Subject Classification ID: 03C45
Mathematics Subject Classification ID: 03C35
zbMATH DE Number: 3957073
zbMATH Keywords: categoricity
zbMATH Keywords: omega-stability
zbMATH Keywords: countable model
Wikidata QID: Q122977793
reviewed by: Jörg Flum
MaRDI profile type: Publication
cites work: Countable models of nonmultidimensional ℵ0-stable theories
cites work: The number of countable models
cites work: A proof of Vaught's conjecture for \(\omega\)-stable theories
full work available at URL: https://doi.org/10.1007/bf02760643
OpenAlex ID: W2384937180
description: scientific article; zbMATH DE number 3957073