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Canonical Functions: a proof via topological dynamics (1610.09660v3)
Published 30 Oct 2016 in math.CO, cs.CC, math.DS, and math.LO
Abstract: Canonical functions are a powerful concept with numerous applications in the study of groups, monoids, and clones on countable structures with Ramsey-type properties. In this short note, we present a proof of the existence of canonical functions in certain sets using topological dynamics, providing a shorter alternative to the original combinatorial argument. We moreover present equivalent algebraic characterisations of canonicity.