Timeline for How dangerous are set-size assumptions?
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 6, 2019 at 2:28 | vote | accept | Pace Nielsen | ||
| Jun 24, 2019 at 15:04 | comment | added | Timothy Chow | By the way, in case you missed it, this MO question might interest you: mathoverflow.net/questions/331441/… | |
| Jun 21, 2019 at 17:17 | comment | added | Timothy Chow | @PaceNielsen : I would suggest Torkel Franzén's book Inexhaustibility: A Non-Exhaustive Treatment, especially Chapter 7, which gives a detailed explanation of arithmetical truth. | |
| Jun 21, 2019 at 15:54 | comment | added | Pace Nielsen | @TimothyChow Thank you for this answer. Would you have a good reference where I can learn more about (and the explicit definition of) arithmetical soundness and/or soundness in general? | |
| Jun 21, 2019 at 12:55 | comment | added | cody | "No meta-theorem of this sort is known" Or, indeed, possible, since Con(ZFC) is a $\Pi^0_1$ statement already! | |
| Jun 21, 2019 at 2:46 | history | edited | Timothy Chow | CC BY-SA 4.0 |
added 165 characters in body
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| Jun 21, 2019 at 2:44 | comment | added | Timothy Chow | Whoops! I mean that ZFC + universes could prove ¬Con(ZFC+universes). | |
| Jun 21, 2019 at 2:43 | comment | added | Noah Schweber | "For example, it is conceivable that under these hypotheses, ZFC + universes could prove ¬Con(ZFC)." That's definitely false: ZFC + universes proves Con(ZFC), so if ZFC + universes is consistent it can't prove $\neg$Con(ZFC). | |
| Jun 21, 2019 at 2:40 | history | answered | Timothy Chow | CC BY-SA 4.0 |