Krivine's intuitionistic proof of classical completeness (for countable languages) (Q1887656)
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scientific article; zbMATH DE number 2117326
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Krivine's intuitionistic proof of classical completeness (for countable languages) |
scientific article; zbMATH DE number 2117326 |
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Krivine's intuitionistic proof of classical completeness (for countable languages) (English)
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22 November 2004
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The first part of the paper presents Krivine's intuitionistic version of Gödel's completeness theorem for first-order classical predicate logic [see \textit{J. L. Krivine}, Bull. Symb. Log. 2, 405--421 (1996; Zbl 0872.03004)]. The second part makes use of the ideas of Krivine's proof to derive intuitionistically some suitable variants of the two following classical theorems: the Ultrafilter Theorem for countable Boolean algebras and the Maximal Ideal Theorem for countable rings.
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first-order classical logic
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Gödel's completeness theorem
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intuitionistic completeness
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ultrafilter theorem
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maximal ideal theorem
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0.8758417
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0.8648213
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0.8626054
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0.8557332
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0.8502905
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