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The Partition Principle does not imply Choice

Source: github.com/openai/math/tree/main/preprints/The-Partition-Pr…

OpenAI

OpenAI Mathopenai-math/The-Partition-Principle-does-not-imply-ChoiceSep 24, 2026math.LOAI-generatedscore 0 · 🔥 4 posts

We prove that the Partition Principle does not imply the Axiom of Choice: if ZF is consistent, then so is ZF with the Partition Principle, Choice for ordinal-indexed families, and the negation of the Axiom of Choice. Separately, over every countable transitive model of ZFC, we construct a transitive symmetric model of this theory with the same ordinals and no new countable sequences of ground elements.

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