[Home]Definable principal congruences

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A (quasi)variety K of algebraic structures has first-order definable principal (relative) congruences (DP(R)C) if there is a first-order formula φ(u,v,x,y) such that for all A ∈ K we have (x,y) ∈ CgK(u,v)  ⇔   A  |=  φ(u,v,x,y).

Here θ = CgK(u,v) denotes the smallest (relative) congruence that identifies the elements u,v, where "relative" means that A/θ ∈ K.

Properties that imply DP(R)C

Equationally definable principal (relative) congruences

Properties implied by DP(R)C

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Last edited July 29, 2003 10:01 pm (diff)