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location Jerusalem, Israel
age 28
visits member for 4 years, 10 months
seen Jun 24 '13 at 21:03
I'm a PhD student at the Hebrew University of Jerusalem. My prime interest is in set theory. More specifically, my research is in forcing theory and its interactions with (higher) descriptive set theory. I'm also interested in model theory, especially Shelah's non-structure theory, abstract model theory, AEC and set-theoretic aspects.

Sep
24
awarded  Autobiographer
Mar
21
awarded  Yearling
Oct
29
awarded  Popular Question
May
24
asked Amalgamation of two ccc algebras may collapse the continuum
Jun
14
comment Blackbox Theorems
Another result of Shelah which may fit in this list is the Main Gap Theorem.
May
16
comment How badly does compactness fail in $\mathcal{L}_{\omega_1\omega}$?
If you weaken your demands to just having the upward Lowenheim-Skolem property, then Morley proved that the Hanf number of $L_{\omega_1, \omega}$ is $\beth_{\omega_1}$.
Jan
26
awarded  Yearling
Nov
20
comment The purview or scope of set theory qua set theory
This is not exactly an answer, but I think that this text might be relevant to your question: shelah.logic.at/files/E16.pdf
Oct
2
comment Why are some axioms preserved in generic extensions?
It's worth noting that the answer may depend on large cardinal assumptions. For example, by a result of Woodin, the existence of class many measurable Woodin cardinals implies that Sigma-2-1 formulas that are true in one forcing extension are true in all forcing extensions satisfying CH (see the paper of Illias Farah for further discussion).
Aug
26
answered The concept of Duality
Jul
31
comment Dual covering theorem
Thanks, Andres. :)
Jul
31
accepted Dual covering theorem
Jul
30
revised Dual covering theorem
added 70 characters in body
Jul
30
asked Dual covering theorem
May
9
comment Most memorable titles
How can we talk about sweetness without mentioning Saccharinity? shelah.logic.at/files/859.pdf :)
Jan
26
awarded  Yearling
Nov
26
comment The history of Proper Forcing
I believe that the initial motivations for proper forcing are well explained throughout Shelah's book. If you want a brief look at the evolution of the subject, a good place to start reading at is the "Proper forcing" chapter in the handbook of set theory (written by Uri Abraham). Regarding the open problems, you can check this paper: shelah.logic.at/files/666.pdf
Nov
21
comment Characterizing forcings that don't add any dominating reals
@Stefan: Yes, it means "there is no f in V dominating the new real". @Justin: The above result relies quite strongly on the absoluteness properties of Suslin forcing. I'm not aware of a similar result without any definability assumption.
Nov
21
answered Characterizing forcings that don't add any dominating reals
Oct
2
comment $\kappa$-scales and the continuum
As Francois mentioned, b=d implies the existence of a scale. Now, it's worth noting that Martin's axiom implies the above equality (hence the existence of a scale).