Random amalgamation of simple theories (Q2707070)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Random amalgamation of simple theories |
scientific article |
Statements
28 August 2001
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amalgamation
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simple theories
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Random amalgamation of simple theories (English)
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The paper under review deals with two (complete) simple theories \(T_1\) and \(T_2\) in disjoint languages \(L_1\) and \(L_2\), and examines the following question: Is there any (complete) simple theory \(T\) extending \(T_1 \cup T_2\) in \(L_1 \cup L_2\)? The author provides a positive answer when \(T_1\) eliminates the quantifier \(\exists^{\infty}\), and \(T_2\) has \(U\)-rank 1 and satisfies \(\operatorname {acl}(A) = A\) for every subset \(A\) (notice that this implies that \(T_2\) eliminates \(\exists^{\infty}\) as well).
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