MATHEMATICS

On the Galois connection for closed classes of infinitary functions

N. L. Poliakov^a, M. V. Shamolin<sup>b

a</sup> National Research University Higher School of Economics, Moscow
^b Lomonosov Moscow State University

Abstract: In this paper, Galois theory is developed for closed sets of functions of any ordinal arity. The classical theorem on Galois-closed classes of functions and sets of predicates on finite sets is transferred to the general case.

Keywords: infinitary function, closed class, clone, Galois connection.

UDC: 510.8, 512.571, 510.227

Received: 20.08.2025
Revised: 22.09.2025
Accepted: 22.09.2025

DOI: 10.7868/S3034504925050188

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