Weak distinction and the optimal definition of causal continuity

TL;DR

This paper introduces feeble distinction, a new causality property that can replace the traditional distinction condition in defining causal continuity, providing new characterizations and implications within causality theory.

Contribution

It proposes feeble distinction as a weaker alternative to distinction in causal continuity and explores its properties and relationships with reflectivity.

Findings

Feeble distinction can replace distinction in causal continuity.

Feeble distinction and reflectivity imply weaker forms of distinction.

New characterizations of weak distinction and reflectivity are provided.

Abstract

Causal continuity is usually defined by imposing the conditions (i) distinction and (ii) reflectivity. It is proved here that a new causality property which stays between weak distinction and causality, called feeble distinction, can actually replace distinction in the definition of causal continuity. An intermediate proof shows that feeble distinction and future (past) reflectivity implies past (resp. future) distinction. Some new characterizations of weak distinction and reflectivity are given.