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

My Shelah number is 2.


1d
asked Reinhardt cardinals and iterability
2d
comment A Question Regarding the Powerset Size Axiom
Maybe the paper A Combinatorial Principle Equivalent to the Existence of Non-free Whitehead Groups by Eklof-Shelah be relevant.
Oct
20
comment A question on Gandy-Jensen system and the rudimentary functions
Isn't sufficient to show that these functions produce Godel operators?
Oct
19
comment On $V$-decisive and weakly homogeneous forcings
I think you mean a $V-$decisive which is not weakly homogeneous?
Oct
19
revised Canonical functions in set theory and their applications
deleted 310 characters in body
Oct
19
asked Canonical functions in set theory and their applications
Oct
16
awarded  forcing
Oct
15
answered Can the Cohen forcing collapse cardinals?
Oct
15
comment non(Meager) in Random times Random extension
Isn't Random$\times$Random, the same as two step iteration of Random. If so, then just use your above comment two times!
Oct
14
comment How to change the successor of a singular with a Woodin?
I am assuming GCH in the ground model, so for all $n<\omega, 2^{\aleph_n} < \aleph_{\omega+1},$ so no bounded subsets of $\aleph_n$ are added. It follows that no bounded subsets of $\aleph_\omega$ are added.
Oct
12
revised How to change the successor of a singular with a Woodin?
added 523 characters in body
Oct
12
comment How to change the successor of a singular with a Woodin?
I think we face some problems. For example if $G$ is $\mathbb{P}_{<\kappa}-$generic, then $V_\kappa$ is not in $Ult(V, G),$ so we may face problems. Another note is that if we want well-foundedness of $Ult(V, G)$ we need more, maybe a Woodin cardinal. I will add more to my answer.
Oct
12
answered Consequences of ZFC+“$|x|\lt|y| \rightarrow |2^x|\lt|2^y|$”
Oct
12
revised How to change the successor of a singular with a Woodin?
added 238 characters in body
Oct
12
comment How to change the successor of a singular with a Woodin?
Completely Jonsson cardinals have very low consistency strength. For example if a cardinal is measurable, then it is Completely Jonsson and there are unboundedly Completely Jonsson cardinals below it.
Oct
12
answered How to change the successor of a singular with a Woodin?
Oct
9
comment A Question Regarding the Powerset Size Axiom
What I understood from the problem is that it asks if we can have a proper class of models of PSA+every W-group is free, and a proper class of models of $\neg PSA+$there are non-free W-groups.
Oct
9
answered A Question Regarding the Powerset Size Axiom
Oct
9
comment A Question Regarding the Powerset Size Axiom
For your last question, the answer is yes. If V satisfies GCH, then V satisfies PSA and we can easily force $\lnot$PSA just by adding $\aleph_2-$many Cohen reals
Oct
7
revised Boolean Valued Models of PA
added 1118 characters in body