Timeline for Closure properties of transitive classes when forcing with $\kappa^+$-cc forcing
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Dec 30, 2016 at 1:03 | comment | added | Cesare | More precisely, the evaluation of $op(\eta,\nu_\eta)$ by $G$ is $op(\eta,\nu_\eta)_G=\langle \eta, X_\eta\rangle$. Since every $A_\nu$ meets $G$ then the evaluation of $\bigcup_\eta\{\{op(\eta,\nu_\eta)\}\times A_\eta\}$ is the function $\{\langle \eta,X_\eta\rangle:\;\eta\in \kappa\}$. | |
| Dec 30, 2016 at 0:53 | comment | added | Cesare | It's the name for an ordered pair. I used that to build a name for the sequence $(X_\eta)_\eta$. | |
| Dec 29, 2016 at 19:16 | comment | added | Noah Schweber | @Cesare What is "op"? | |
| Dec 29, 2016 at 19:08 | comment | added | Cesare | Thank you @NoahSchweber !! But only one more thing: the name for the sequence $(X_\eta)_\eta$ would be $\bigcup_\eta \{\{op(\eta,\nu_\eta)\}\times A_\eta\}$? | |
| Dec 29, 2016 at 19:02 | vote | accept | Cesare | ||
| Dec 29, 2016 at 18:53 | history | edited | Noah Schweber | CC BY-SA 3.0 |
added 1160 characters in body
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| Dec 29, 2016 at 18:46 | comment | added | Noah Schweber | @Cesare I was totally wrong, see Miha's comment above. I'm editing my answer now. | |
| Dec 29, 2016 at 18:45 | comment | added | Cesare | Of course, Cummings' chapter from the Handbook. It's on page 804. | |
| Dec 29, 2016 at 18:43 | comment | added | Miha Habič | There is a subtle issue here: each of the names $\nu_\eta$ is in $M$, but the whole sequence only lives in $V[G]$. You need the extra assumptions on $\mathbb{P}$ to get the sequence itself (or a good enough approximation) in $V$. | |
| Dec 29, 2016 at 18:39 | comment | added | Cesare | That was my problem... I reached your same proof but I don't know where $\kappa^+-$cc-ness is expected to appear.. | |
| Dec 29, 2016 at 18:34 | history | answered | Noah Schweber | CC BY-SA 3.0 |