This article presents a critical–propositional analysis of Olav Mitchell Underdal’s The Omega Number System: Toward a Graded Transarchimedean Extension of Complex Analysis (2025), published on Zenodo under DOI https://doi.org/10.5281/zenodo.15164708, in dialogue with the Theory of Objectivity (TO). The study examines possible compatibilities and tensions between Underdal’s graded transarchimedean system and the modal-ontological discipline of TO, especially regarding logical Nothing, boundary, zero, infinitesimals, infinitary magnitudes, singularities, regularization, Inducer Effects, phenomenic thresholds, and informational transcendence. The article argues that Underdal’s proposal is formally relevant because it recognizes the insufficiency of the classical domain for dealing with zero, infinity, divergence, and multiple scales. At the same time, it maintains that the Omega system does not replace the modal axioms or the cosmogonic theorem of the Theory of Objectivity. This analysis received analytical support from ChatGPT. Keywords: Theory of Objectivity; Vidamor Cabannas; Denivaldo Silva; Olav Mitchell Underdal; Omega Number System; transarchimedean ontology; modal ontology; logical Nothing; infinitesimals; infinity; zero; singularities; regularization; Inducer Effects; phenomenic thresholds; informational transcendence; atomic radiation; cosmological Eras; scientific dialogue.
Cabannas et al. (Sun,) studied this question.