2
votes
1answer
47 views

Normal ultrafilters on $\mathcal{P}_{\kappa}(\lambda)$

I am looking at fine normal ultrafilters on $\mathcal{P}_{\kappa}(\lambda)$ and I have seen that there are two (seemingly) different formulations of normality, in terms of regressive (sometimes also ...
5
votes
1answer
122 views

Injective or constant function on measurable cardinal

I'm working on the following question: Let $\kappa$ regular cardinal, and $f:\kappa \rightarrow \kappa$. Prove that $\{\alpha < \kappa\mid f|_\alpha : \alpha \rightarrow \alpha\}$ is a ...
8
votes
1answer
174 views

If $\kappa$ is measurable, does there exist a normal measure on $\mathcal P_{\kappa}(\kappa)$?

I'm trying to do exercise $10.7$ of Jech's Set Theory: If $\kappa$ is a measurable cardinal, then there exists a normal measure on $\mathcal P_{\kappa}(\kappa)$. For a set $A$, with $|A|\geq ...
5
votes
1answer
337 views

Normal ultrafilters and Stationary sets

If $\kappa$ is a measurable cardinal, and $\mathcal{U}$ is a normal ultrafilter which is $\kappa$-complete then $\mathcal{U}$ extends the club filter (i.e. every club is a member of $\mathcal{U}$). ...