Set-theoretic status of the collection of universes in probability assignments

Ascertain whether the collection of universes considered when assigning measures or probabilities (e.g., in level IV multiverse contexts) forms a set within standard set theory or instead constitutes a proper class, in order to ground measure-theoretic formalizations (sigma-algebras and Kolmogorov axioms) for events defined as entire universes.

Background

The paper critiques attempts to assign probabilities to the hypothesis that we are living in a simulation by raising foundational measure-theoretic concerns. Specifically, it questions how to define sigma-algebras and probability measures over collections whose elements are entire universes.

The author explicitly notes uncertainty about whether the collection of universes is even a set, as opposed to a proper class, which directly affects the feasibility of assigning Kolmogorov-consistent measures and evaluating probabilities in a rigorous mathematical framework.