Reversibility of disconnected structures

A relational structure is called reversible iff every bijective endomorphism of that an automorphism. We characterize property in the class disconnected binary structures, and one its subclasses—posets are disjoint union chains. Also, using concept a monotone function from structures preordered by monomorphism into well founded relation, we detect additional classes posets. further give equivalents reversibility some special unions For example, CSB linear orders limit type prove such poset corresponding sequence order types finite-to-one. also show $$\sigma $$ -scattered poset, whenever bi-embedability