The Partition Principle does not imply Choice
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.
Comments and reviews
No comments yet.
Discussed elsewhere
API
curl /api/v1/records/openai-math/The-Partition-Principle-does-not-imply-Choice
curl -X POST /api/v1/records/openai-math/The-Partition-Principle-does-not-imply-Choice/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/openai-math/The-Partition-Principle-does-not-imply-Choice/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"body": "…", "review": true}'
OpenAI, the Partition Principle, and mathematicskaragila.orgAsaf Karagila
By the time I got out of bed yesterday, I had three people ask me if I'd seen the OpenAI announcement that the Partition Principle does not (...)