Functional monadic ortholattices and locally finite $\sigma$-free polyadic ortholattices

TL;DR

This paper proves that all monadic ortholattices can be represented functionally and introduces locally finite σ-free polyadic ortholattices, extending the functional representation to these structures.

Contribution

It establishes a functional isomorphism for monadic ortholattices and introduces a new class of locally finite σ-free polyadic ortholattices with similar representation results.

Findings

Monadic ortholattices are isomorphic to functional ortholattices.

Locally finite σ-free polyadic ortholattices have a functional representation.

Addresses a recent open question by Harding.

Abstract

In this paper, we show that every monadic ortholattice is isomorphic to a functional one, thereby resolving a recent question posed by Harding. We then study certain substitution-free reducts of the polyadic ortholattices, which we call locally finite $\sigma$-free polyadic ortholattices, and provide an analogous functional representation result.