## Posets isomorphic to their extensions.(English)Zbl 0575.06003

An isomorphism $$f: P\to Q$$ of a poset P onto a collection Q of its lower ends, or, down-closed subsets of P (ordered by inclusion) is said to be recycling if $$Y\in Q$$ implies $$\cup_{y\in Y}f(y)\in Q$$. Consequences of the existence of recycling isomorphisms are investigated. For example, if Q contains all lower ends of well-ordered subsets of P, then P satisfies the ascending-chain condition, and Q is the set of all principle ideals of P.