Finite axiomatizability and theories with trivial algebraic closure (Q1183711)
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scientific article; zbMATH DE number 33577
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Finite axiomatizability and theories with trivial algebraic closure |
scientific article; zbMATH DE number 33577 |
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Finite axiomatizability and theories with trivial algebraic closure (English)
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28 June 1992
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It is shown that every quasi-finitely axiomatized complete theory with trivial algebraic closure has the strict order property or is the theory of an indiscernible set. The author conjectures that every finitely axiomatized \(\omega\)-categorical theory with infinite models has the strict order property. It is also shown that complete theories with trivial algebraic closure and (for example) no quantifier-free unstable formulas are rather limited.
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complete theory
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trivial algebraic closure
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strict order property
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theory of an indiscernible set
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0.90513724
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0.90295434
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0.90153843
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