Function classes and relational constraints stable under compositions with clones

TL;DR

This paper refines a Galois theory for functions and relational constraints by introducing algebraic conditions on relations, enhancing the theoretical framework for understanding stability under compositions with clones.

Contribution

It introduces algebraic conditions on relations to refine the Galois theory for functions and relational constraints over arbitrary sets.

Findings

Enhanced theoretical framework for stability under compositions

Refined Galois correspondence with algebraic conditions

Broader applicability to arbitrary sets

Abstract

The general Galois theory for functions and relational constraints over arbitrary sets described in the authors' previous paper is refined by imposing algebraic conditions on relations.