12,256 reputation
341105
bio website boolesrings.org/asafk
location Israel
age 30
visits member for 4 years, 11 months
seen 39 mins ago

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 [cohen-forcing] 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
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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 choice-y 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