Undecidability of some elementary theories over PAC fields (Q1074575)
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scientific article; zbMATH DE number 3948241
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Undecidability of some elementary theories over PAC fields |
scientific article; zbMATH DE number 3948241 |
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Undecidability of some elementary theories over PAC fields (English)
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1986
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We consider the theory of the field \(\tilde Q\) of algebraic numbers equipped with \(n\geq 2\) automorphisms \(\sigma_ 1,...,\sigma_ n\). We show that with probability 1 (in the sense of Haar measure on Gal\((\tilde Q/Q))\) this theory has the complexity of arithmetic. We use torsion points on elliptic curves to encode finite sets. The methods work also in nonzero characteristic.
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absolute Galois group
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normalized Haar measure
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algebraic number
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field
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pseudo algebraically closed field
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arithmetic
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torsion points on elliptic curves
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