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A survey of clones on infinite sets

Martin Goldstern·Michael Pinsker
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Abstract

A clone on a set X is a set of finitary operations on X which contains all projections and which is moreover closed under functional composition. Ordering all clones on X by inclusion, one obtains a complete algebraic lattice, called the clone lattice. We summarize what we know about the clone lattice on an infinite base set X and formulate what we consider the most important open problems.

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Martin Goldstern, Michael Pinsker. 2008-01-15. A survey of clones on infinite sets. https://arxiv.org/abs/math/0701030

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