Galois connection for sets of operations closed under permutation, cylindrification and composition

Details Galois connection for sets of operations closed under permutation, cylindrification and composition Galois connection for sets of operations closed under permutation, cylindrification and composition

2009-10-28

arxiv.org/abs/0910.5409v3

Mathematics

Rings and Algebras

22 pages; Section 4 added

Scientific paper

We consider sets of operations on a set A that are closed under permutation of variables, addition of dummy variables and composition. We describe these closed sets in terms of a Galois connection between operations and systems of pointed multisets, and we also describe the closed sets of the dual objects by means of necessary and sufficient closure conditions. Moreover, we show that the corresponding closure systems are uncountable for every A with at least two elements.

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