Timeline for Namba forcing and semiproperness
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 14, 2019 at 10:46 | answer | added | Andreas Lietz | timeline score: 5 | |
| Apr 29, 2016 at 15:11 | vote | accept | Todd Eisworth | ||
| Apr 28, 2016 at 15:35 | answer | added | Sean Cox | timeline score: 13 | |
| May 5, 2014 at 21:45 | comment | added | Todd Eisworth | The question of whether SCC implies Namba semiproperness seems interesting, though, and not unreasonable! | |
| May 5, 2014 at 21:39 | comment | added | Philip Welch | @Todd, Martin: V. sorry to be misleading, I should have written ``shown to be implied by the semiproperness of Namba..." in my comment. I don't know that SCC and semiproperness of Namba are equivalent. Mea culpa. So it looks like we only know that both semi-properness of Namba and SCC are somewhere between measurability and ramseyness? | |
| May 5, 2014 at 0:50 | comment | added | Todd Eisworth | Philip: I know he shows that the strong Chang conjecture is a consequence of Namba semimproperness in Theorem XII.2.5 of the book. Is SCC actually equivalent? | |
| May 4, 2014 at 11:34 | comment | added | Goldstern | Theorem 2.2. in "PIF" says that Namba is semiproper (equivalently: there is some semiproper forcing changing $cf(\omega_2^V)$ to $\omega$) iff player II has a winning strategy in this game: In step $n$, Player I chooses a function $F_n:\omega_2\to \omega_1$, and Player II replies with a value $i_n<\omega_1$. In the end, let $i_\infty:=\sup\{i_n:n \in \omega\}$. Player II wins iff the set $\{\, t\in \omega_2: \sup\{ F_n(t):n\in\omega\}\le i_\infty\,\}$ is unbounded. | |
| May 4, 2014 at 7:04 | comment | added | Philip Welch | In: "Greatly Erdős cardinals with some generalizations to the Chang and Ramsey properties" APAL,Vol 162,2011 Ian Sharpe and I show that the Strong Chang Conj. (shown equiv. to the semiproperness of Namba by Shelah in his book) implies the consistency of a Ramsey cardinal. So somewhere between measurability and Ramsey... | |
| May 4, 2014 at 5:51 | comment | added | Andrés E. Caicedo | Hi Todd. This is a good question. John Krueger may know something about this. | |
| May 4, 2014 at 3:42 | history | asked | Todd Eisworth | CC BY-SA 3.0 |