On finitely generated reducts of polyadic equality algebras

TL;DR

This paper explores the generation properties of certain algebraic structures related to polyadic equality algebras, revealing differences between finite and infinite dimensional cases and extending previous results.

Contribution

It extends a key result by Andreka and Nemeti, showing new limitations on finite generation of weak set quasi-polyadic simple algebras.

Findings

Existence of finitely generated weak set quasi-polyadic simple algebras of dimension >1 that cannot be singly generated.

Contrasting results for polyadic algebras of infinite dimension.

Differences between dimension complemented and non-complemented cases.

Abstract

Extending a deep result of Andreka and Nemeti, we show that unlike the dimension complemented case, there are weak set quasi-polyadic simple algebras of dimension >1, that are finitely genertaed with more than one element, but cannot be generated with a single element. We give a contrasting result for polyadic agebras of infinite dimension.