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Maximal clones on uncountable sets that include all permutations

Michael Pinsker
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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.

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Michael Pinsker. 2005-05-14. Maximal clones on uncountable sets that include all permutations. https://arxiv.org/abs/math/0401103

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