Preprint in the OpenAI Math release
The Partition Principle does not imply Choice
OpenAI
Abstract
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.
open until 1 Jan 2028
est. 50% chance this result is independently verified by the end of 2027.
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