Classification of semi-algebraic \(p\)-adic sets up to semi-algebraic bijection (Q2754271)
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scientific article; zbMATH DE number 1670925
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Classification of semi-algebraic \(p\)-adic sets up to semi-algebraic bijection |
scientific article; zbMATH DE number 1670925 |
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11 November 2001
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semi-algebraic \(p\)-adic set
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semi-algebraic isomorphism
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0.91170603
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0.8914342
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0.8899729
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0.8890058
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Classification of semi-algebraic \(p\)-adic sets up to semi-algebraic bijection (English)
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Let~\(K\) be a finite extension of~\({\mathbb Q}_p\). A subset of~\(K^n\) is said to be semi-algebraic if it is a finite Boolean combination of projections of affine \(K\)-varieties. A semi-algebraic subset of some~\(K^n\) has a well defined dimension [see \textit{P. Scowcroft} and \textit{L. van den Dries}, J. Symb. Logic 53, No. 4, 1138-1164 (1988; Zbl 0692.14014)]. NEWLINENEWLINENEWLINEIn the paper under review, the author proves that two infinite semi-algebraic subsets are semi-algebraically isomorphic if and only if they have the same dimension. The main ingredient is a ''rectilinearization'' theorem.
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