II.T43 — Structural Incompatibility of Unique Omega and Archimedean Density

Under K5, properties (U) unique global omega and (A) Archimedean local density cannot both hold. (A) implies not-(U) via the cardinality hierarchy; (U) + K5 implies not-(A) via the Inapplicability Theorem (I.T35) and Unique Infinity (I.T36).