The Ontological Volume of the Multiverse: Definition and Boundaries of the Concept

The article introduces and formalizes the concept of the "ontological volume of the multiverse" (Ω). This concept was used in previous works of the MBM (Models of the Infinite-Dimensional Multiverse) series implicitly — as a "single volume" or "complete set of elements of reality" — but did not receive a rigorous definition. It is shown that Ω is not physical space-time. It is a set of potential elements of reality, from which a certain sample A(S) is activated in each universe, where S is the ontological selector. Formally: Ω = {e₁, e₂, e₃, …} and A(S) = P(S)(Ω). Space-time T(S) is a property of the activated set A(S), not a property of Ω. Each universe has its own space-time; these space-times are not "lying" in a common space but are different ways of connecting the elements of Ω. A comparison is conducted with the concepts of mathematical democracy (Tegmark, Level IV), the logical matrix (SDH), and the infosphere (Floridi). It is shown that Ω is not a mathematical structure, not a logical matrix, and not an informational environment, but an ontological possibility. Mathematical structures, logical conditions, and information are merely types of elements that may be contained in Ω. The connection of Ω with other concepts of the series is determined: the "Universes Here" model (a change of S as a sample from Ω), HPSR (folds as stable configurations of A(S)), and modulational interaction (the external factor X acts on A(S), not on Ω). Open questions are formulated: whether Ω is finite or infinite; whether it can be formalized mathematically (set theory, category theory, topos theory); and how Ω relates to EFOS. The definition of Ω removes the confusion between "place" and "possibility": universes are not located "somewhere," they are different ways of activating the elements of Ω.