bio  website  math.ipm.ac.ir/golshani 

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PostDoctoral 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 1216, 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asked  On an unpublished result of Magidor 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 