Timeline for Are Cohen Generics Minimal Covers?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 1 at 12:40 | comment | added | Peter Gerdes | @JoelDavidHamkins Thanks, I was getting a bit confused because it ends up being true that exactly the opposite is true effectively (every n generic is a Turing minimal cover of an n-generic..n >1) but I presume this is basically the non-atomless case ruled out by the stronger closure conditions in full set theoretic forcing. | |
| Nov 17 at 20:23 | comment | added | Joel David Hamkins | It's because every subforcing of a countable forcing notion is countable, hence is itself Cohen forcing. | |
| Nov 17 at 4:44 | comment | added | François G. Dorais | No worries Peter! All good! | |
| Nov 17 at 4:08 | vote | accept | Peter Gerdes | ||
| Nov 17 at 4:08 | comment | added | Peter Gerdes | I was thinking that if you knew why that claim was true off the top of your head you'd respond and otherwise you'd ignore it. Sorry if it felt like I was expecting you to solve my problem. Anyway, I finally managed to download something from libgen that was labeled right and figured it out. Thanks for the citatoin | |
| Nov 17 at 4:02 | comment | added | François G. Dorais | That's a pretty common problem when reading papers from 38 years ago. I'm not sure what you're expecting me to do about that. | |
| Nov 17 at 3:52 | comment | added | Peter Gerdes | Unfortunately, the part I'm having trouble with is the very first theorem. That if a is cohen generic and 0 < x < a then x is of cohen generic degree. The paper cites to Jech but I only have the 3rd edition and I don't think it preserved the numbers since the cited results don't seem obviously related. | |
| Nov 17 at 1:57 | history | answered | François G. Dorais | CC BY-SA 4.0 |