On closed sets of relational constraints and classes of functions closed under variable substitutions

TL;DR

This paper extends Pippenger's Galois theory of finite functions and relational constraints to infinite sets, broadening the theoretical framework to include functions with infinite domains and codomains.

Contribution

It generalizes the existing Galois theory to infinite sets, allowing for a more comprehensive understanding of relational constraints and functions in infinite contexts.

Findings

Extended Galois theory to infinite sets

Applicable to functions with infinite domains and codomains

Provides a theoretical foundation for infinite relational constraints

Abstract

Pippenger's Galois theory of finite functions and relational constraints is extended to the infinite case. The functions involved are functions of several variables on a set $A$ and taking values in a possibly different set $B$, where any or both of $A$ and $B$ may be finite or infinite.