Atomistic and orthoatomistic effect algebras

TL;DR

This paper characterizes atomistic effect algebras, explores conditions for orthoatomistic structures, and provides examples distinguishing different classes of effect algebras and posets.

Contribution

It introduces new characterizations of atomistic and orthoatomistic effect algebras, including conditions under which they are equivalent or distinct.

Findings

Weakly orthocomplete Archimedean atomic effect algebra is orthoatomistic

An example of an orthoatomistic orthomodular poset that is not weakly orthocomplete

New characterizations of atomistic and orthoatomistic effect algebras

Abstract

We characterize atomistic effect algebras, prove that a weakly orthocomplete Archimedean atomic effect algebra is orthoatomistic and present an example of an orthoatomistic orthomodular poset that is not weakly orthocomplete.