A proof of Vaught's conjecture for \(\omega\)-stable theories
type: Item
instance of: scholarly article
title: A proof of Vaught's conjecture for \(\omega\)-stable theories
zbMATH Open document ID: 0584.03021
DOI: 10.1007/BF02760651
author: S. Shelah
author: Michael Makkai
author: Leo Harrington
published in: Israel Journal of Mathematics
publication date: 1984-01-01T00:00:00Z
review text: The famous Vaught's conjecture is the statement that for any countable theory T in \(L_{\omega_ 1\omega}\) the number of isomorphism types of countable models of T is either \(2^{\aleph_ 0}\) or at most \(\aleph_ 0\). The question is still open even for theories in finitary logic. In the paper under review Vaught's conjecture is proved for T a first-order countable complete \(\omega\)-stable theory. The results of the paper are due to Shelah.
Mathematics Subject Classification ID: 03C45
Mathematics Subject Classification ID: 03C15
zbMATH DE Number: 3935015
zbMATH Keywords: omega-stable theory
zbMATH Keywords: countable theory
zbMATH Keywords: countable models
Wikidata QID: Q56551495
reviewed by: Oleg Belegradek
MaRDI profile type: Publication
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cites work: Q3931364
description: scientific article; zbMATH DE number 3935015