Post complete and 0-axiomatizable modal logics (Q920977)
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scientific article; zbMATH DE number 4164807
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Post complete and 0-axiomatizable modal logics |
scientific article; zbMATH DE number 4164807 |
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Post complete and 0-axiomatizable modal logics (English)
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1990
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A modal logic is said to be Post complete if it has no proper consistent extensions. The Post number p(L) of a logic L is the cardinal of the set of all Post complete extensions of L. The author proves that for any n, \(1\leq n\leq 2^{\aleph_ 0}\), there exist \(2^{\aleph_ 0}\) normal modal logics with Post number equal to n. The investigation is done via the study of dual spaces of free algebras without generators over the varieties of modal algebras.
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modal logic
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Post complete
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Post number
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Post complete extensions
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normal modal logics
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free algebras
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modal algebras
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