Maximal clones on uncountable sets that include all permutations

Details Maximal clones on uncountable sets that include all permutations Maximal clones on uncountable sets that include all permutations

2004-01-10

arxiv.org/abs/math/0401103v3

Mathematics

Rings and Algebras

19 pages; latest version has shorter proofs and no mistakes

Scientific paper

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.

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