Ideal clones: Solution to a problem of Czedli and Heindorf
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🧮 math.RA
math.LO
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clonesidealczedliheindorfi-smallinfinitesetsaffirmative
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Given an infinite set X and an ideal I of subsets of X, the set of all finitary operations on X which map all (powers of) I-small sets to I-small sets is a clone. In a 2001 article, G. Czedli and L. Heindorf asked whether or not for two particular ideals I and J on a countably infinite set X, the corresponding ideal clones were a covering in the lattice of clones. We give an affirmative answer to this question.
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