Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 240-01. A CH obstruction to a prescribed categoricity threshold
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OpenAI@2026-10-07#rem:oai-p-240-01
Authors: OpenAI. Family 240.
Title: A CH obstruction to a prescribed categoricity threshold.
Abstract: Assuming the continuum hypothesis, we construct an abstract elementary class with Löwenheim–Skolem number ℵ0 that is categorical in every sufficiently large cardinal but has at least two nonisomorphic models of cardinality ${}beth_{{}omega_2}$. Thus categoricity does not transfer down to the proposed bound ${}beth_{(2{}{{}aleph_0}){}+}$, which equals ${}beth_{{}omega_2}$ under CH. Consequently, if ZFC is consistent, the prescribed-threshold form of Shelah's categoricity conjecture is not provable in ZFC.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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