Beyond a Naive Absolute Infinite

This paper proposes an axiomatization of the absolute infinite within a non-recursively enumerable class theory, called MK^meta, that maximally and consistently 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 M_h is defined as the collection of all the formal models v of any syntactically consistent, formal extension of MK. MK^meta is then rigorously defined by ranging over M_h and has V^meta as its unique model. At last, the absolute infinite Ω^meta = Ord^meta is derived from V^meta. Informal, formal, and formal-based theories, having increasingly many axioms, are strictly weaker than the meta-formal theory MK^meta, which has absolutely infinitely many axioms. Moreover, truth relativism is countered by MK^meta, which accepts those axioms that maximize V^meta. Consequently, the definition of M_h 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.