Timeline for "Relative plausibility" of some infinitary theories
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 27, 2021 at 20:09 | history | edited | Noah Schweber | CC BY-SA 4.0 |
added 138 characters in body
|
| Jun 25, 2021 at 17:07 | history | edited | Noah Schweber | CC BY-SA 4.0 |
added 125 characters in body
|
| Jun 25, 2021 at 16:57 | history | edited | Noah Schweber | CC BY-SA 4.0 |
deleted 567 characters in body
|
| Jun 9, 2021 at 20:50 | history | edited | Noah Schweber | CC BY-SA 4.0 |
deleted 91 characters in body
|
| Jun 9, 2021 at 20:19 | comment | added | Noah Schweber | @FarmerS Meeting some "large" but still countable set of dense subsets for the relevant forcing. E.g. the notions of $n$-generic (for Cohen forcing) in computability theory. A lot of the time we don't need full set-theoretic genericity. | |
| Jun 9, 2021 at 20:17 | comment | added | Farmer S | What does "sufficiently (Sacks) generic" mean? | |
| S Apr 15, 2021 at 18:58 | history | bounty ended | CommunityBot | ||
| S Apr 15, 2021 at 18:58 | history | notice removed | CommunityBot | ||
| Apr 10, 2021 at 22:44 | history | edited | Noah Schweber | CC BY-SA 4.0 |
added 100 characters in body
|
| S Apr 7, 2021 at 15:19 | history | bounty started | Noah Schweber | ||
| S Apr 7, 2021 at 15:19 | history | notice added | Noah Schweber | Draw attention | |
| Apr 4, 2021 at 22:48 | comment | added | LSpice | I always get nervous about links that don't announce their target, since Elsevier likes to shuffle their organisation. "Barwise compactness" points to the eponymous chapter, namely Chapter 9, of Model theory for infinitary logic, edited by Keisler. | |
| Apr 4, 2021 at 22:47 | history | edited | LSpice | CC BY-SA 4.0 |
\mathit
|
| Apr 4, 2021 at 22:14 | comment | added | Noah Schweber | Furthermore, $\Sigma_1(L_{\omega_1})$-ness is absolute in both directions, so the set of plausible theories doesn't change when we force. This means that each generic extension $L[G]$ yields a corresponding quotient of $\mathcal{Plaus}$ where we replace "generic extension of $L$" by "generic extension of $L[G]$." "Forcing quotients" of $\mathcal{Plaus}$ might be a useful thing to think about along the way to an answer to the specific question above. But this is all just guesswork. | |
| Apr 4, 2021 at 22:12 | comment | added | Noah Schweber | Separately it's worth noting that making an originally-unsatisfiable theory become satisfiable is really the only impact forcing can have here: by absoluteness of $\mathcal{L}_{\omega_1,\omega}$-satisfaction we can never make a satisfiable theory unsatisfiable, and by downward Lowenheim-Skolem for individual $\mathcal{L}_{\omega_1,\omega}$-sentences + Mostowski absoluteness we can never make an unsatisfiable countable theory satisfiable. | |
| Apr 4, 2021 at 22:07 | history | edited | Noah Schweber | CC BY-SA 4.0 |
added 762 characters in body
|
| Apr 4, 2021 at 18:19 | history | asked | Noah Schweber | CC BY-SA 4.0 |