Clones above the unary clone

Abstract

Let c be the cardinality of the continuum. We give a family of pairwise incomparable clones (on a countable base set) 2c members, all with the same unary fragment, namely the set of all unary operations. We also give, for each n, a family of 2c clones all with the same n-ary fragment, and all containing the set of all unary operations.

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