Generalizations of Tarski's fixed point theorem for order varieties of complete meet semilattices
type: Item
instance of: scholarly article
title: Generalizations of Tarski's fixed point theorem for order varieties of complete meet semilattices
zbMATH Open document ID: 0674.06006
DOI: 10.1007/BF00353657
published in: Order
publication date: 1989-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 06A12
zbMATH DE Number: 4103141
zbMATH Keywords: order preserving function
zbMATH Keywords: order variety
zbMATH Keywords: u-conditionally complete poset
zbMATH Keywords: fixed point sets of monotonic functions
zbMATH Keywords: retracts
author: Joel Berman
author: W. J. Blok
reviewed by: Ki Hang Kim
MaRDI profile type: Publication
cites work: Generalized arithmetic
cites work: Q5341481
cites work: Q3853685
cites work: A structure theory for ordered sets
cites work: On the existence of optimal fixpoints
cites work: Q3730636
cites work: Outline of a Theory of Truth
cites work: Chain-complete posets and directed sets with applications
cites work: A note on axiomatizable order varieties
cites work: Order varieties generated by \(\vee\)-semilattices of finite width
cites work: The strong selection property and ordered sets of finite length
cites work: A lattice-theoretical fixpoint theorem and its applications
cites work: Four valued semantics and the Liar
cites work: Completeness in Semi-Lattices
Recommended article: Q4876701
Recommended article: An order theoretic approach in fixed point theory
Recommended article: Generalizations of semiorders: A review note
Recommended article: Semilattices of ordered compactifications
Recommended article: Q4231898
Recommended article: A generalization of the Tarski-Seidenberg theorem, and some nondefinability results
Recommended article: Q3495401
Recommended article: On the \(t \)-equivalence of generalized ordered sets
Recommended article: On elementary theories of semilattices of partial orders on sets
Recommended article: Order theoretic variants of the fundamental theorem of compact semigroups
description: scientific article; zbMATH DE number 4103141