Timeline for Normal measures on $P_{\kappa }(\lambda )$ extend the club filter

6 events

when toggle format	what		by	license	comment
Apr 9, 2011 at 15:48	vote	accept	Amit Kumar Gupta
Apr 8, 2011 at 22:47	answer	added	Jason		timeline score: 2
Apr 8, 2011 at 21:06	comment	added	Amit Kumar Gupta		The first question in the comment above is not so serious though; for the application I'm interested in I'm happy to assume $j : V \to M$ arises from some fine measure, say $U'$, on $P_{\kappa}(\lambda)$.
Apr 8, 2011 at 21:04	comment	added	Amit Kumar Gupta		Hi oktan. Why does the fineness of $U$ give us said closure property of $M$? We're obtaining $U$ from $j : V \to M$, not vice versa. Also, sorry this may be a basic question, but how do we know $\lambda ^{<\kappa} < j(\kappa)$?
Apr 8, 2011 at 19:11	comment	added	Stefan Hoffelner		A partial answer for 2 and 3: As the ultrafilter $U$ is a fine measure we even have $M^{\lambda^{<\kappa}} \subset M$, and as $D \in M^{\lambda^{<\kappa}}$ we know that $D \in M$ (See Prop 22.11. in Kanamoris Book for a proof of this). Moreover as $M$ is transitive and $V$ thinks that the size of $C$ = size of $D$ $\le \lambda^{<\kappa} < j(\kappa)$, $M$ thinks that the size of $D$ is less than $j(\kappa)$. So both things that you wanted to accept 2 and 3 are done.
Apr 8, 2011 at 15:58	history	asked	Amit Kumar Gupta	CC BY-SA 3.0