Timeline for Silver's unpublished work on reverse Easton iteration
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 2, 2014 at 18:43 | comment | added | Asaf Karagila♦ | @Joel: Yes!!! Let's do that! | |
| Sep 2, 2014 at 11:44 | comment | added | Joel David Hamkins | The "reverse" terminology goes way back -- I'm not sure who started it -- but it is increasingly on the way out. I made an argument against it at the Berkeley Logic Colloquium in the mid-1990s, and I remember walking backwards across the stage and then forwards to illustrate the point, with Silver, Woodin, Solovay and others in the audience. | |
| Sep 2, 2014 at 11:27 | comment | added | Mohammad Golshani | @JoelDavidHamkins Thanks for your comment. Do you know who first used the name "reverse Easton iteration" for such kind of forcing iterations. Something maybe related to your note is the use of lemma for Jensen's covering theorem (Jensen's covering lemma); while it is a very deep theorem (and in fact Kanamori says it the most important theorem of set theory in 1970th). | |
| Sep 2, 2014 at 11:10 | comment | added | Joel David Hamkins | My opinion is that it should not be called "reverse", and we should all abandon that old terminology. The proper distinction is between an Easton-support product and an Easton-support iteration; in both cases we use support in the Easton ideal. Moreover, the Easton-support iteration is more forward than it is reversed, since you are taking the posets from the later stages as the iteration progresses. (This would be "reverse" only if one imagines walking through the iteration while facing backwards.) Please call this the Easton-support iteration, which accurately describes the ideal. | |
| Sep 2, 2014 at 6:20 | comment | added | Mohammad Golshani | Maybe one reason is the following: Easton forcing can be imagined as an iteration from upward to downward (for example the product of $Add(\omega, \omega_2)\times Add(\omega_1, \omega_3)$ can be imagined as a two step iteration first with $Add(\omega_1, \omega_3)$ followed by $Add(\omega, \omega_2)$ (and you can not reverse the iteration). But in reverse Easton iteration, the iteration is from downward to upward. So you are reversing the kind of iteration!!!!! | |
| Sep 2, 2014 at 6:11 | comment | added | Asaf Karagila♦ | I never understood the reason for it to be called "reverse". | |
| Sep 2, 2014 at 4:53 | history | asked | Mohammad Golshani | CC BY-SA 3.0 |