bio  website  boolesrings.org/asafk 

location  Israel  
age  30  
visits  member for  4 years, 11 months 
seen  39 mins ago  
stats  profile views  9,245 
Born and raised in Israel. Ph.D. student in the Hebrew university in Jerusalem; studying set theory.
2d

reviewed  Approve Periodicity of any fermat number modulo a prime 
2d

comment 
Does $Add(\kappa,1)^L$ ever collapse cardinals?
(I removed the [cohenforcing] tag, I think it's overly specific.) 
2d

revised 
Does $Add(\kappa,1)^L$ ever collapse cardinals?
edited tags 
2d

comment 
Does $Add(\kappa,1)^L$ ever collapse cardinals?
@Nate: It's the forcing $\operatorname{Add}(\kappa,1)$ (all the partial functions from $\kappa\to2$ with domain bounded below $\kappa$; ordered by reverse inclusion), but only those functions which are in $L$. 
May 19 
comment 
Looking for reference or proof to some facts stated on Anand Pillay's book
I bet you didn't expect that to happen. 
May 15 
revised 
History of Tarski's problems on free groups
edited tags 
May 15 
comment 
If two structures are elementarily equivalent, is there a zigzag of elementary embeddings between them?
@Emil: Seeing how BPIT+Los imply choice, the answer is a resounding no. 
May 15 
comment 
If two structures are elementarily equivalent, is there a zigzag of elementary embeddings between them?
What's wrong with overkills? If you are not careful, and you only underkill something, it will come back to haunt you. Haven't you watched '80s horror films to learn that? :) 
May 11 
comment 
Formulating Kunen's inconsistency and Reinhardt cardinals in term of category theory
@Andreas: Now I feel less guilty for not thinking about $\sf KM$ as something with global choice included. :) 
May 10 
comment 
Formulating Kunen's inconsistency and Reinhardt cardinals in term of category theory
@Joel: Kinda surprised to see you omitted $\sf KM$! :) 
May 10 
comment 
Formulating Kunen's inconsistency and Reinhardt cardinals in term of category theory
@David: I merely wanted to point out that if we are referring to possible cases that elementary embeddings and ultrapowers are not quite as nicely behaved as in $\sf ZFC$, these two papers should be mentioned. :) 
May 10 
revised 
Formulating Kunen's inconsistency and Reinhardt cardinals in term of category theory
deleted 2 characters in body 
May 10 
comment 
Formulating Kunen's inconsistency and Reinhardt cardinals in term of category theory
@David: One link and another link are probably worth a mention here. 
May 10 
comment 
What consistency results follow the assumption: $\forall\alpha(\aleph_{\alpha+1}\nleq2^{\aleph_\alpha})$?
That's an interesting question. I think that the issue here is similar to supercompactness. While "useful" is something that seem to imply a strong connection to aleph cardinals (e.g. $\mathcal P_\kappa(\lambda)$ rather than $P_\kappa(X)$ for arbitrary $X\geq\kappa$); these are often notably weaker than their choicey counterparts. 
May 10 
comment 
What consistency results follow the assumption: $\forall\alpha(\aleph_{\alpha+1}\nleq2^{\aleph_\alpha})$?
If it's weaker than a subcompact, then it cannot be supercompact! :) 
May 9 
comment 
What consistency results follow the assumption: $\forall\alpha(\aleph_{\alpha+1}\nleq2^{\aleph_\alpha})$?
Trevor, I think that depends on the definition of "supercompact". 
May 9 
comment 
What consistency results follow the assumption: $\forall\alpha(\aleph_{\alpha+1}\nleq2^{\aleph_\alpha})$?
Proper class of those? 
May 9 
comment 
What consistency results follow the assumption: $\forall\alpha(\aleph_{\alpha+1}\nleq2^{\aleph_\alpha})$?
Thanks, that's interesting. Do you have some educated guess to make (mine is that $(\bullet)$ is roughly equiconsistent with a proper class of Woodin cardinals). 
May 9 
comment 
What consistency results follow the assumption: $\forall\alpha(\aleph_{\alpha+1}\nleq2^{\aleph_\alpha})$?
Awesome. Is $(\bullet)$ somewhat a known axiom, or can you just say these things because of some obvious consequences like failure of the covering lemma for all sort of inner models? 
May 8 
revised 
What consistency results follow the assumption: $\forall\alpha(\aleph_{\alpha+1}\nleq2^{\aleph_\alpha})$?
edited body 