Triple Representation Theorem for orthocomplete homogeneous effect algebras

TL;DR

This paper investigates the structure of certain effect algebras by analyzing their key element sets and proves a significant representation theorem for a class of these algebras, enhancing understanding of their foundational properties.

Contribution

It introduces a comprehensive study of meager, sharp, and central elements in meager-orthocomplete homogeneous effect algebras and establishes a Triple Representation Theorem for sharply dominating cases.

Findings

Characterization of meager, sharp, and central elements in the algebra

Proof of the Triple Representation Theorem for the specified class

Enhanced structural understanding of orthocomplete homogeneous effect algebras

Abstract

The aim of our paper is twofold. First, we thoroughly study the set of meager elements $M(E)$, the set of sharp elements $S(E)$ and the center $C(E)$ in the setting of meager-orthocomplete homogeneous effect algebras $E$. Second, we prove the Triple Representation Theorem for sharply dominating meager-orthocomplete homogeneous effect algebras, in particular orthocomplete homogeneous effect algebras.