Maximal clones on uncountable sets that include all permutations
Rings and Algebras
2007-05-23 v3 Logic
Abstract
We first determine the maximal clones on a set X of infinite regular cardinality which contain all permutations but not all unary functions, extending a result of Heindorf's for countably infinite X. If |X| is countably infinite or weakly compact, this yields a list of all maximal clones containing the permutations since in that case the maximal clones above the unary functions are known. We then generalize a result of Gavrilov's to obtain on all infinite X a list of all maximal submonoids of the monoid of unary functions which contain the permutations.
Keywords
Cite
@article{arxiv.math/0401103,
title = {Maximal clones on uncountable sets that include all permutations},
author = {Michael Pinsker},
journal= {arXiv preprint arXiv:math/0401103},
year = {2007}
}
Comments
19 pages; latest version has shorter proofs and no mistakes