Timeline for Reverse-mathematical strength of Banach-Tarski
Current License: CC BY-SA 4.0
5 events
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| Dec 14, 2023 at 7:38 | comment | added | Mikhail Katz | C7X, thanks for the clarification. You may want to elaborate a bit on the interesting issue concerning ZF+DC. Here as you know Solovay is not sufficient because of the IC hypothesis, but an additive total measure can be constructed anyway. | |
| Dec 13, 2023 at 17:55 | comment | added | C7X | @MikhailKatz When originally posting I may have had too broad of a question in mind, with the intended goal being to optimize on "two fronts" (both weakening the base theory and weakening the choice assumption), rather than a reversal to a standard theorem. This may be too ambitious, so I will refocus and rephrase the post. The question of weakening the necessary choice assumption seems to already be better-documented, so I will ask about weakening the base theory. | |
| Dec 13, 2023 at 13:09 | comment | added | Mikhail Katz | It's not too clear what you are asking. Are you asking whether Banach-Tarski reverses to some other standard axiom/theorem over some system weaker than ZF? Or are you asking what the minimal version of Choice is that would be needed to prove Banach-Tarski? | |
| Dec 13, 2023 at 8:17 | history | edited | C7X | CC BY-SA 4.0 |
In case $\mathbb R$ partitionable into more than $\beth_1$ pieces
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| Dec 13, 2023 at 7:37 | history | asked | C7X | CC BY-SA 4.0 |