On probabilistic elimination of generalized quantifiers (Q2748424)
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scientific article; zbMATH DE number 1659413
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On probabilistic elimination of generalized quantifiers |
scientific article; zbMATH DE number 1659413 |
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On probabilistic elimination of generalized quantifiers (English)
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4 November 2002
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generalized quantifiers
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almost sure quantifier elimination
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convergence laws
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zero-one laws
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Let \(Q\) be a collection of generalized quantifiers. The author gives a convenient characterization for the cases where the logic \(L^\omega_{\infty\omega}(Q)\) has almost sure quantifier elimination [in the sense of \textit{Yu. V. Glebskij}, \textit{D. I. Kogan}, \textit{M. I. Liogon'kij} and \textit{V. A. Talanov}, Kibernetika 1969, No. 2, 17-27 (1969; Zbl 0209.30803) and \textit{R. Fagin}, J. Symb. Log. 41, 50-58 (1976; Zbl 0341.02044)]. The results provide a method to prove zero-one and convergence laws for these logics. The paper contains many extensions of known zero-one laws.
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