In a prior posting about generalizing $\sf DC$ and $\sf AC_\omega$, the answer mentioned many versions of choice. Now of those versions, which ones fail to entail Banach-Tarski "B-T" paradox? I know that AC$_\omega$, and DC doesn't prove it, but what about the other versions? What is the strongest among those versions that fails to prove B-T paradox?
2026-04-08 09:46:12.1775641572
Which versions of choice fail to prove Banach-Tarski paradox?
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