Quantifier Elimination in Trans-Finite Xenoglossy: Deriving the Semantic Isomorphisms of Non-Convergent Abyssal Idiolects via the Stability Spectrum of Uncountable Elder-Theories

Mathematical Applications of Science Fiction We present a rigorous derivation of quantifier elimination for a class of non-convergent, transfinite linguistic structures designated as Abyssal Idiolects. By modeling these idiolects as models of an uncountable theory within the framework of continuous logic and stability theory, we demonstrate that the semantic ambiguity inherent in Class-IV informational hazards can be resolved through a generalized Tarski–Seidenberg theorem. We introduce the Stability Spectrum for Elder Theories and prove that if an idiolect is stable for sufficiently large cardinality, then every formula in the infinitary language is equivalent to a quantifier-free formula modulo the base theory. This establishes a computable isomorphism between the syntactic structure of xenoglossic transmissions and the constructible sets of a definable topology, effectively solving the translation problem for entities residing in orthogonal time streams. We conclude with applications to the theoretical containment of memetic singularities.