On the categoricity theorem in \(L_{\omega _ 1\omega}\) (Q1095888)
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scientific article; zbMATH DE number 4029521
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the categoricity theorem in \(L_{\omega _ 1\omega}\) |
scientific article; zbMATH DE number 4029521 |
Statements
On the categoricity theorem in \(L_{\omega _ 1\omega}\) (English)
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1986
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Let T be a countable theory in \(L_{\omega_ 1\omega}\). For each infinite cardinal \(\kappa\) we denote by I(\(\kappa\),T) the number of pairwise non-isomorphic models of T in \(\kappa\). In this paper we prove the following theorem: If \(I(\omega_ 1,T)=1\) and the models of T in \(\omega_ 1\) are \(L_{\omega_ 1\omega}\)-homogeneous then \(I(\kappa,T)=1\) for all \(\kappa >\omega\).
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classification
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number of pairwise non-isomorphic models
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