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Reconstruction theorems for semigroups of functions which contain all transpositions of a set and for clones with the same property

We prove that if S is a set of functions from a set A to itself, S is closed under composition, and S contains all transpositions of A, then the action of S on Acan be recovered from the semigroup consisting of S together with its compositionoperation. We also prove the analogous statement for clones.

preprint2016arXivOpen access
Jonah MaisselMatatyahu Rubin
math.LO
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Jonah MaisselMatatyahu Rubin

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