First-order definable retraction problems for posets and reflexive graphs
A retraction from a structure P to its substructure Q is a homomorphism from P onto Q that is the identity on Q. We present an algebraic condition which completely characterzies all posets and all reflexive graphs Q such that the class of all posets or reflexive graphs, respectively, that admit a retraction onto Q is first-order definable.
first-order definability retraction posets graphs homomorphism