Timeline for Non-set-theoretic consequences of forcing axioms
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 13, 2020 at 10:07 | comment | added | Asaf Karagila♦ | One can view the axiom of choice as a forcing axiom. | |
| Dec 12, 2020 at 23:15 | comment | added | bof | If their solution requires fancy set-theoretic axioms then they are set theory even if they were disguised as algebra or topology. | |
| Dec 11, 2020 at 2:40 | answer | added | Erik Walsberg | timeline score: 3 | |
| Dec 9, 2020 at 21:02 | comment | added | Timothy Chow | @JordanMitchellBarrett : They are not; I guess I was mainly responding to Sam Hopkins. | |
| Dec 9, 2020 at 20:47 | comment | added | Jordan Barrett | @TimothyChow are these consequences or uses of forcing axioms though? | |
| Dec 9, 2020 at 20:17 | comment | added | Sam Hopkins | @TimothyChow: ah, thanks for the link! | |
| Dec 9, 2020 at 19:24 | comment | added | Timothy Chow | There is already an MO question about Forcing as a tool to prove theorems. | |
| Dec 9, 2020 at 18:28 | comment | added | Sam Hopkins | @KamerynWilliams: that's very interesting! Shelah's answer to the Erdos-Hajnal question about $K_4$-free edge-coloring is particularly striking. You could possibly write this as an answer. | |
| Dec 9, 2020 at 18:24 | comment | added | Julia Williams | @SamHopkins One genre of argument is the forcing + absoluteness argument. That is, you force to make P true and then you show that P had to be true in the ground model all along, thus proving P from ZFC (or whatever axioms you started with). This talk by Assaf Rinot and this talk by Matteo Viale both give overviews of the technique and give some examples of how it's been used. | |
| Dec 9, 2020 at 13:17 | history | became hot network question | |||
| Dec 9, 2020 at 6:37 | comment | added | Andrés E. Caicedo | @Jordan This is common in point-set topology. There are also many examples from algebra (group theory, or the theory of modules.) | |
| Dec 9, 2020 at 5:42 | comment | added | Jordan Barrett | Secondary question: have we seen adoption of forcing axioms by any non-set-theorists in order to prove results in their field? | |
| Dec 9, 2020 at 5:30 | comment | added | Sam Hopkins | Even more strongly one could ask, are there examples of using the technique/philosophy of forcing to show something other than that a particular statement is independent of ZFC (or a closely related logical system). | |
| Dec 9, 2020 at 5:27 | answer | added | Mohammad Golshani | timeline score: 14 | |
| Dec 9, 2020 at 5:12 | history | asked | Jordan Barrett | CC BY-SA 4.0 |