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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.
Reviewer: J.Adámek

MSC:

06B23 Complete lattices, completions
06A06 Partial orders, general
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