Model_Theoretic_Collapse

This paper establishes that model-theoretic plurality collapses under enforced admissibility. When standing preservation is treated as a binary, fail-closed constraint, the usual freedom to move between multiple models, interpretations, or semantic realizations is shown to be illusory rather than foundational. The analysis demonstrates that apparent coexistence of distinct models depends on illicit assumptions: hidden parameter variation, silent scope shifts, or deferred admissibility evaluation. Once these moves are excluded, only a single admissible representational structure remains up to internal redescription. Alternative models either reduce to notational variants or fail admissibility outright. The result fixes model-theoretic collapse as a structural consequence, not a limitation of expressive power or formalism. It explains why semantic underdetermination and model multiplicity cannot survive admissibility enforcement. The paper introduces no semantics, logics, or model-building procedures. It records an exhaustion result showing that admissible reasoning admits no genuine plurality of models.