General algebraic systems Varieties Concept
Lattice of equational theories
Summary
The lattice of equational theories of a signature is the set of all equational theories of that signature, ordered by inclusion. An equational theory is a set of identities closed under logical consequence. This lattice is complete, and it is dually isomorphic to the lattice of all varieties of the signature, because larger theories have fewer models. It can be described as the lattice of fully invariant congruences of a term algebra on countably many variables.
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| Tag | 2R8QQTP1CE |
|---|---|
| URI | m2://2R8QQTP1CE |
| Kind | concept |
| Writing | W0 stub |
| MSC | 08B15, 08B05, 03C05 |
| Changed | 2 November 2026 |
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