Some highly undecidable lattices (Q584255)
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scientific article; zbMATH DE number 4134029
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some highly undecidable lattices |
scientific article; zbMATH DE number 4134029 |
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Some highly undecidable lattices (English)
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1990
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The main result of this paper is: If an algebraically closed field K has infinite transcendence degree over its prime field, then the first-order theory of the lattice of K's algebraically closed subfields has the logical complexity of full second-order logic on the set K. A similar, although not as strong, result is also proved for the more general setting in which the role of K is filled by a Steinitz exchange system.
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lattice of algebraically closed subfields
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algebraically closed field
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first-order theory
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logical complexity
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Steinitz exchange system
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