Generalizations of Tarski's fixed point theorem for order varieties of complete meet semilattices
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.
scientific article; zbMATH DE number 4103141
scientific article