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Post-Doctoral Research Fellow, School of Mathematics, Institute for Research in Fundamental Sciences (IPM).

My Shelah number is close to one!.


IPM Conference on Set Theory and Model Theory, October 12-16, 2015.


1d
asked On an unpublished result of Magidor
2d
comment Tree property and singular strong limit cardinals
@Avshalom Thanks for the link.
2d
accepted Tree property and singular strong limit cardinals
Aug
30
comment On generic forcing conditions
You can prove the following, to prove the fact you are looking for: if $p$ is $(M, P)$-generic and $\dot{r}$ is such that $p \Vdash \dot{r}=(r_0,\dot{r}_1) \in M \cap P*\dot{Q}, r_0 \in \dot{G}_0$, then there is $\dot{q}$ such that $(p, \dot{q})$ is $(M, P*\dot{Q})$-generic and $(p, \dot{q})\Vdash ``\dot{r}\in \dot{G} $''.
Aug
30
comment A question regarding strong cardinals and measure sequence
@JingZhang But in the argument above, we do not need $u_j \restriction \beta \in M'.$ We talk about models $M_n$, and they include all required information. Am I missing with something?
Aug
30
comment Tree property and singular strong limit cardinals
Thank you for the reference.
Aug
21
comment A question regarding strong cardinals and measure sequence
But why it should lead to a contradiction?
Aug
21
comment A question regarding strong cardinals and measure sequence
Note that $Ult(V, E')$ is essentially the direct limit of a sequence obtained using measures $E'(a), a \in [\kappa+1]^{<\omega.}$
Aug
21
comment A question regarding strong cardinals and measure sequence
You have stated the ultrapower by $E'$ is essentially the same as the ultrapower by $U(0).$ This can not be true, as the first one can for example include $V_{\kappa+2}$ while the second can not (assuming $GCH$).
Aug
21
comment A question regarding strong cardinals and measure sequence
But note that $u_j(0)=\kappa,$ and $u_j(1)$ is what you called $U(0).$ Clearly $u_j(0) \in Ult(V, E').$
Aug
21
answered A question regarding strong cardinals and measure sequence
Aug
20
comment A question regarding strong cardinals and measure sequence
Note that in Gitik's paper the sequence $\bar{U}$ is defined recursively, and is not an arbitrary sequence of ultrafilters. The key point in Gitik's construction is that, using the embedding induced by $E'$, say $i: M \to M',$ he defines a new measure sequence which is easily seen its restrictions to ordinals less than $\alpha,$ to be in $M'$, and then shows by induction that the measure sequence below $\alpha$ is essentially the same as this new measure sequence constructed using $i$. Now everything should be clear.
Aug
8
comment Reverse of a termspace forcing fact
In the paper "THE APPROXIMATION PROPERTY AND THE CHAIN CONDITION" a generalization of Unger's result is presented. See Lemma 1.5 there.
Jul
31
accepted Consistency strength of being strong cardinal and indestructible under collapses
Jul
31
comment Consistency strength of being strong cardinal and indestructible under collapses
Thanks a lot. It essentially answers what I had in mind.
Jul
30
asked Consistency strength of being strong cardinal and indestructible under collapses
Jul
29
revised Collapsing the cardinals between two singular cardinals
deleted 3 characters in body
Jul
29
revised Collapsing the cardinals between two singular cardinals
added 895 characters in body
Jul
29
comment Collapsing the cardinals between two singular cardinals
But in $V[H], \kappa$ is singular of cofinality $\omega,$ and passing from $V[H]$ to $V[G],$ we are collapsing all cardinals in the interval $(\kappa, \kappa^{+\omega}]$ without collapsing other cardinals, and both of this cardinals are already singular in $V[H].$
Jul
28
answered Collapsing the cardinals between two singular cardinals