A survey of clones on infinite sets
classification
🧮 math.RA
math.LO
keywords
clonelatticeclonesinfinitewhatalgebraicbasecalled
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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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