True Axiomatic Limit (⇰⏁) is a Dhaxarum-class number and variant of the original Axiomatic Limit that actually lives up to it's name; as the true, inaccessible limit of all higher-order transcendental axioms. The "weak" version (also called Evolved Axiomatic Limit), denoted as "ω⏁", is simply the fixed point of the Beyond Axiom function originally described within the BAO article (mathematically expressed as K = BA(K)). However, the rest of this article will discuss the "strong" version of True Axiomatic Limit and how it exceeds the Beyond Axiom Ordinal.
Extensible Transaxiomatic Function[]
The Extensible Transaxiomatic Function (abbreviated as ETF) is an extension of the original Beyond Axiom function designed to accomodate transcendental forms of logic. It is denoted as a function ∃Ψ(n), where "n" is the index of the function itself. ∃Ψ(0) is 0, ∃Ψ(1) is Omnifinity, and ∃Ψ(2) is ω⏁ (Evolved Axiomatic Limit). In other words, ∃Ψ(n+1) is the fixed point of all mathematical and metaphysical axioms that apply to ∃Ψ(n). True Axiomatic Limit is defined as ∃Ψ(Э) using this function, however higher Axiomatic Limits can potentially be achieved by extending the original ETF to become an array notation similar to that used for the Small Ignorance Ordinal.