Existentially Definable Factor Congruences
Pedro S\'anchez Terraf
TL;DR
This paper investigates the conditions under which factor congruences in algebraic varieties are definable by existential formulas, establishing a link to their compactness in all algebras of the variety.
Contribution
It proves that if factor congruences are definable by an existential formula, then they are compact in every algebra of the variety.
Findings
Existential definability of factor congruences implies their compactness.
Factor congruences can be characterized by first-order formulas with central elements.
The paper establishes a necessary and sufficient condition for definability of factor congruences.
Abstract
A variety V has definable factor congruences if and only if factor congruences can be defined by a first-order formula Phi having central elements as parameters. We prove that if Phi can be chosen to be existential, factor congruences in every algebra of V are compact.
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