2006/12/31 by Martin Goldstern, Goldstern, Martin, Michael Pinsker +1
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #math.LO #math.RA #msc:08A05 #msc:08A40
paper · pdf · doi:10.48550/arxiv.math/0701030
37 pages
arxiv created 2008/01/15 · arxiv updated 2009/12/01
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.