General algebraic systems Quasivarieties and model classes Concept
Quasivariety
Summary
A quasivariety is a class of algebras of one signature that is axiomatized by quasi-identities. Every variety is a quasivariety, but quasivarieties need not be closed under homomorphic images. By Mal'cev's characterization, they are the classes closed under isomorphic copies, subalgebras, direct products and ultraproducts. They are the algebraic counterpart of universal Horn logic and appear in algebraic logic, where many logics are described by quasivarieties rather than varieties.
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| Tag | WRXEKT4NQS |
|---|---|
| URI | m2://WRXEKT4NQS |
| Kind | concept |
| Writing | W0 stub |
| MSC | 08C15, 03C52 |
| Specializes | Prevariety, Universal Horn class |
| Same as | |
| Changed | 2 November 2026 |
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