12,632 reputation
344110
bio website boolesrings.org/asafk
location Israel
age 30
visits member for 5 years, 2 months
seen 4 hours ago

Born and raised in Israel. Ph.D. student in the Hebrew university in Jerusalem; studying set theory.


7h
comment Properties of Coefficients of Order Polynomials
There are basic rules to follow when posting a question on several sites. The first one being: Don't order pizza from two places at once just because you're hungry.
7h
comment Properties of Coefficients of Order Polynomials
I'm voting to close this question as off-topic because this already has an answer on MSE.
18h
comment Why should we care about “higher infinities” outside of set theory?
@Alexis: I know a few actual finitists, and they generally hold the belief that there are infinitely many natural numbers, but there is no such thing as "the set of natural numbers". In some sense, they work in ZFC where the axiom of infinity is replaced by its negation. What you're alluding to is probably described as Ultrafinitism.
19h
revised Precise interpretability strength of $\mathcal P_{DF}(\omega)$ and $L_{\omega_1^{CK}}$
added 2 characters in body
1d
comment Why should we care about “higher infinities” outside of set theory?
Can you phrase the title in a less antagonizing fashion?
Aug
24
comment Consistency of the nonrigidity of $P(\omega_1)/NS$
Also, it's funny. It's not just as Yair pointed out about lifting the automorphisms; it's also the consequence of the answer Paul gave you yesterday on MSE. :-)
Aug
23
comment Consistency of the nonrigidity of $P(\omega_1)/NS$
@Yair: Ah yes, that is the much easier example! Originally we thought (of a known example, as it turned out) of the collapse [to $\omega$] of the first $\aleph$-fixed point using a tree where each point has a distinct number of successors. The idea here is similar.
Aug
23
comment Important formulas in Combinatorics
@Incnis Mrsi: Nothing is wrong, really. But it feels less natural than addition and multiplication of cardinals, since it causes you to pause and think "Which one is larger?", and then realize the result is actually irrelevant. Whereas addition/multiplication works better since it's just a constant term.
Aug
23
comment Consistency of the nonrigidity of $P(\omega_1)/NS$
Diamond and squares. Perhaps adding a generic automorphism using an $\omega_2$-closed forcing, if this can be done.
Aug
22
comment Consistency of the nonrigidity of $P(\omega_1)/NS$
(I mean, my guess is as good as any. But if you walked into my office, and asked me this, I'd ask two questions "Is it true/false in $L$, and is it true/false after adding sufficiently many Cohen reals to $L$?", and after we (both of us, if you haven't got the answers prepared in advance) have answers to these, we might be starting on a path to a more concrete answer.)
Aug
22
comment Large Cardinal Principles that Imply $\Sigma_3^1$-Generic Absoluteness
It was mentioned in a course about generic absoluteness and stationary tower forcing, and was attributed to Martin-Solovay. No concrete reference was given, or else I would have probably post it as an answer.
Aug
22
comment Consistency of the nonrigidity of $P(\omega_1)/NS$
I have no idea. It was right off the bat. Because Cohen reals themselves are quite malleable, and the forcing will have plenty of automorphisms. Maybe some of them "seep through".
Aug
22
comment Consistency of the nonrigidity of $P(\omega_1)/NS$
Just off the bat, add $\omega_1$ Cohen reals to $L$?
Aug
22
comment Defining Global Choice in terms of strong limit cardinals over $ZF$
Why do you expect that there will be such a way?
Aug
22
comment Large Cardinal Principles that Imply $\Sigma_3^1$-Generic Absoluteness
If my memory serves me right, a measurable implies $\Sigma^1_3$-absoluteness for forcing smaller than the measurable. So the existence of a proper class of measurable cardinals implies $\Sigma^1_3$-absoluteness.
Aug
21
comment Important formulas in Combinatorics
The use of $\max$ is a bit confusing, and it will be clearer, in my opinion, to write $\aleph_\omega^{\aleph_0}<\aleph_{\omega_4}\cdot(2^{\aleph_0})^+$.
Aug
20
comment Important formulas in Combinatorics
Gil, thank you for the reply. I'll try to think about something. Of course $\lambda<2^\lambda$ is too basic and quite uninteresting from a research point of view. But there is new things to be said about infinitary graphs and the like.
Aug
19
comment What other axioms for set theory can be written in the form: “If mathematical structures $X$ and $Y$ are equipotent, then they're isomorphic”?
Over a finite field, if two vector spaces are equipotent then they are isomorphic.
Aug
18
comment Values where infinite products of primes and composites are equal
ImageShack has turned most of its photos into ads. In the process the link to the graph is no longer available. If you have the original photo, you might want to consider uploading it using the SE interface.
Aug
18
comment Important formulas in Combinatorics
Does this allow for set theoretic infinitary combinatorics? :-)