A note on algebraically and existentially closed structures (Q1098869)
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scientific article; zbMATH DE number 4037904
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on algebraically and existentially closed structures |
scientific article; zbMATH DE number 4037904 |
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A note on algebraically and existentially closed structures (English)
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1987
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Theorem 1. If K is a class of algebras and A is algebraically closed with respect to K then A is congruence extensile in K. Theorem 3. Let K be a class closed under finite products and A be existentially closed with respect to K. Then A satisfies \(\Phi (u)=\bigwedge \{\Phi_ i(u)\); \(i=0,...,n\}\) for all primitive formulas \(\Phi\).
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algebraically closed class
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existentially closed class
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positive formula
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congruence extensile
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