Beyond a Naive Absolute Infinite

This paper proposes an axiomatization of the absolute infinite within a non-recursively enumerable class theory, called MKmeta, that maximally extends the formal MK: Morse-Kelley with global choice (GC). Class ordinals and class cardinals avoid the Burali-Forti paradox and GC is assumed to warrant comparability of class cardinals. A Hamkinsian multiverse Mh is defined as the collection of all the models v of any syntactically consistent, formal extension of MK. MKmeta is then rigorously defined by ranging over Mh and has Vmeta as its unique model. At last, the absolute infinite Ωmeta = Ordmeta is derived from Vmeta. Informal, formal, and formal-based theories, having increasingly many axioms, are strictly weaker than the meta-formal theory MKmeta, which has absolutely infinitely many axioms. Moreover, truth relativism is countered by MKmeta, which accepts those axioms that maximize Vmeta. Consequently, the definition of Mh can be used as a rebuttal of both height and width potentialism, when combined with the argument that only the meta-formal level can capture the entire mathematical reality in a single rigid theory.