Generalizations of Tarski's fixed point theorem for order varieties of complete meet semilattices

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1989 English Publisher:Springer Science and Business Media LLCJournal:Order, volume 5, pages 381-392 (issn: 0167-8094, eissn: 1572-9273,

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Authors: Berman, Joel; Blok, W. J.;

doi: 10.1007/bf00353657

Generalizations of Tarski's fixed point theorem for order varieties of complete meet semilattices

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Abstract

A poset is u-conditionally complete if a subset has a least upper bound whenever all its subsets of cardinality less than u have upper bounds. The authors prove that for these posets the set of fixed point sets of monotonic functions coincides with the set of its retracts, which can be described as those u-conditionally complete subposets which are well embedded.

Related Organizations

University of Illinois at Chicago
United States
University of Illinois at Chicago
United States

Keywords

order preserving function, order variety, Semilattices, u-conditionally complete poset, retracts, fixed point sets of monotonic functions

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