Timeline for What fragments of ZF are consistent with a set being equal in size to its power set?
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Aug 25, 2018 at 10:05 | answer | added | Andrej Bauer | timeline score: 9 | |
| Aug 24, 2018 at 22:29 | comment | added | Michal R. Przybylek | @MattF. your comment is not correct. An injection form P(N) to N is not consistent with IZF. The statement that there can be no injection from P(A) to A for any A follows from Cantor's argument, which is purely constructive. Perhaps, you have confused P(N) with $N^N$, or $2^N$... | |
| Aug 24, 2018 at 20:30 | comment | added | Zuhair Al-Johar | @MattF.can you please add this as an answer, and if you know of other versions, then please mention them. | |
| Aug 24, 2018 at 20:16 | comment | added | user44143 | IZF (intutionistic Zermelo-Frankel) is a strong theory, and consistent with an injection from P(N) to N. Such an injection follows from the version of Church’s thesis that “all functions are recursive”. | |
| Aug 24, 2018 at 3:50 | history | edited | user44143 | CC BY-SA 4.0 |
reformatted and emphasized questions
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| Aug 23, 2018 at 23:25 | comment | added | Zuhair Al-Johar | @DavidRoberts thanks | |
| Aug 23, 2018 at 22:29 | comment | added | David Roberts♦ |
You really should use the lo.logic tag, this is the second time I've added it to a question you asked in this area. Also, use \text as a wrapper for when you want text inside a math environment
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| Aug 23, 2018 at 22:28 | history | edited | David Roberts♦ | CC BY-SA 4.0 |
Added lo.logic tag, cleaned up TeX
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| Aug 23, 2018 at 21:26 | comment | added | Zuhair Al-Johar | @GerhardPaseman if for example Con(NF) is proved then we can have a fragment that can interpret $\omega$_order arithmetic and yet be consistent with this notion. To me any fragment near the strength of $PA$ is not to be considered weak. | |
| Aug 23, 2018 at 19:52 | comment | added | Gerhard Paseman | It will have to be weak to keep from forming the set of members y of x which do not belong to f(y), while still having the power to express your notion. Gerhard "Not Sure Of The Utility" Paseman, 2018.08.23. | |
| Aug 23, 2018 at 19:26 | history | asked | Zuhair Al-Johar | CC BY-SA 4.0 |