Timeline for How much choice we can get from this partition principle?
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Feb 11, 2023 at 17:29 | comment | added | Zuhair Al-Johar | @Holo, True! But we may know that something is NOT decidable in a fragment of a theory before we know that for the mother theory. Example $\sf AC , ZFA, ZF$. | |
| Feb 11, 2023 at 14:04 | comment | added | Holo | @ZuhairAl-Johar any proof in stratified-ZF will certainly transfer into ZF, as ZF is an extension of stratified-ZF, so it is also open in stratified-ZF | |
| Feb 11, 2023 at 12:58 | comment | added | Zuhair Al-Johar | @Holo, is that the same for stratified ZF? | |
| Feb 11, 2023 at 11:37 | comment | added | Holo | @ZuhairAl-Johar "it"=WPP=your version of the partition principle, that is: $AC⇒PP⇒CB^*⇒WPP$ and the opposite direction of those arrows are all open in ZF | |
| Feb 11, 2023 at 6:37 | comment | added | Zuhair Al-Johar | @Holo, you mean this version of PP? | |
| Feb 10, 2023 at 23:40 | comment | added | Holo | @ZuhairAl-Johar IIRC, it is open whether it implies the dual CB theorem (which in turns it is open whether the dual CB theorem implies PP and it is open whether PP implies AC) in ZF | |
| Feb 10, 2023 at 22:10 | comment | added | Zuhair Al-Johar | @AsafKaragila, what kind of known forms of choice this entails? Especially from the stratified axioms of $\sf ZF$? | |
| Feb 10, 2023 at 21:58 | history | edited | Zuhair Al-Johar | CC BY-SA 4.0 |
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| Feb 10, 2023 at 21:52 | history | edited | Zuhair Al-Johar | CC BY-SA 4.0 |
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| Feb 10, 2023 at 21:41 | comment | added | Asaf Karagila♦ | This is known as the Weak Partition Principle. | |
| Feb 10, 2023 at 18:31 | comment | added | Zuhair Al-Johar | @AsafKaragila, Yes! In the context of ZF. | |
| Feb 10, 2023 at 17:59 | comment | added | Asaf Karagila♦ | So, every partition of $X$ is either incomparable or injects to $X$? | |
| Feb 10, 2023 at 12:21 | history | asked | Zuhair Al-Johar | CC BY-SA 4.0 |