## On many-sorted algebraic closure operators.(English)Zbl 1038.08001

A well-known theorem of Birkhoff-Frink states that every algebraic closure operator can be realized as the subalgebra operator of an appropriate algebra. However, for many-sorted algebras (i.e. indexed families of sets) an analogous theorem is not longer true. The main theorem of the paper asserts that the corresponding many-sorted closure operators are precisely the uniform algebraic operators.

### MSC:

 08A30 Subalgebras, congruence relations 06A15 Galois correspondences, closure operators (in relation to ordered sets)
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