A proof of Vaught's conjecture for \(\omega\)-stable theories (Q1070222)
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scientific article; zbMATH DE number 3935015
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A proof of Vaught's conjecture for \(\omega\)-stable theories |
scientific article; zbMATH DE number 3935015 |
Statements
A proof of Vaught's conjecture for \(\omega\)-stable theories (English)
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1984
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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.
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omega-stable theory
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countable theory
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countable models
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