Some model-theoretic results in the algebraic theory of quadratic forms (Q5956888)
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scientific article; zbMATH DE number 1713718
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some model-theoretic results in the algebraic theory of quadratic forms |
scientific article; zbMATH DE number 1713718 |
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Some model-theoretic results in the algebraic theory of quadratic forms (English)
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2001
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Some model-theoretic properties of special groups of finite type are studied. Special groups are models of a first-order axiomatization of the algebraic theory of (reduced) binary quadratic forms over fields. They consist of a group \(G\) of exponent \(2\), a distinguished element \(-1\), and an `isometry' relation on pairs from \(G\). Special groups of `finite type' are obtained from finite special groups by a finite number of applications of two kinds of operations: `product' and `extension'. For such groups the notions of elementary equivalence, saturation, elementary embeddings, quantifier elimination, stability, and Morley rank are studied.
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special groups of finite type
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first-order axiomatization
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binary quadratic forms over fields
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Morley rank
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