Hyperimaginaries and automorphism groups (Q2732271)
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scientific article; zbMATH DE number 1623514
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Hyperimaginaries and automorphism groups |
scientific article; zbMATH DE number 1623514 |
Statements
Hyperimaginaries and automorphism groups (English)
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13 January 2003
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first-order logic
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automorphism groups
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hyperimaginaries
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simple theories
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A hyperimaginary is an equivalence class of a type-definable equivalence relation on tuples of possibly infinite length. The notion of hyperimaginary was recently introduced by \textit{B. Hart}, \textit{B. Kim} and \textit{A. Pillay} [ibid. 65, 293-309 (2000; Zbl 0945.03051)], mainly with reference to simple theories. In this paper several issues are considered: on the one hand, various levels of complexity of hyperimaginaries, and when hyperimaginaries can be reduced to simpler hyperimaginaries. On the other hand, the issue of what information about hyperimaginaries in a saturated model \(M\) can be obtained from the abstract group \(\Aut(M)\).
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