First-order theories as many-sorted algebras (Q795823)
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scientific article; zbMATH DE number 3863175
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | First-order theories as many-sorted algebras |
scientific article; zbMATH DE number 3863175 |
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First-order theories as many-sorted algebras (English)
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1984
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This work shows that it is possible to reconstruct fundamental logical notions in the universal algebraic framework. Namely, a first-order theory is expressed as a many-sorted algebra verifying equational axioms and thus Henkin's models, first-order completeness and first order equational calculus are obtained, in purely algebraic style, by using Birkhoff's theorems on varieties.
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algebraic semantics
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first-order theory
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many-sorted algebra
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equational axioms
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Henkin's models
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first-order completeness
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first order equational calculus
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varieties
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