11,765 reputation
337100
bio website boolesrings.org/asafk
location Israel
age 29
visits member for 4 years, 7 months
seen 4 hours ago

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


13h
comment Adding a real with infinite conditions
@François: Awesome. Thanks!
18h
comment Adding a real with infinite conditions
Yes, I will definitely give this more thought. But first I really really really gotta finish banging some argument shut about choiceless forcing (and actually the question here is somewhat related to trying some alternative approach in solving the issue I'm dealing with by changing the forcing a bit). I think I'll drag a couple other Ph.D. students with me to these sort of questions.
18h
comment Adding a real with infinite conditions
I'm sure that it's possible to investigate properties of the new sets inherited from the ideal and the choice of zero or co-positive domains, in a context much more general than ideals on $\omega$ (but I do expect things to get much more complicated, of course... and depend on additional hypotheses like cardinal arithmetics and large cardinals).
18h
comment Adding a real with infinite conditions
Looking at Jech's book it strikes me that we really have two tricks up our sleeve for adding a new subset to some $X$. Fix some ideal on $X$ and forcing with partial functions from $X$ to $2$; either the domains are from the ideal, or the domains are co-positive sets. The ideal of finite sets gives us Cohen in the first case and Prikry-Silver in the latter case.
19h
accepted Adding a real with infinite conditions
19h
comment Adding a real with infinite conditions
Aha! I knew I'd seen it before. And just as luck would have it, I have a copy of that book from the library with me. I wonder why I didn't check it before!
19h
asked Adding a real with infinite conditions
2d
comment algebraic topology and 3d/4d printing
@Ryan: Do you think this question has anything to do with art?
Jan
22
comment Examples of common false beliefs in mathematics
Ohhhh, right. I was thinking about atoms in the sense of Boolean algebra, as minimal positive elements. Thanks for the clarification!
Jan
22
comment Examples of common false beliefs in mathematics
Take any measurable cardinal, then there is an atomless probability measure on its power set. It's just that an event is either improbable or its negation is improbable. Unless by probability measure you mean it obtains many values, not just two.
Jan
22
comment Examples of common false beliefs in mathematics
I think you need $\kappa\leq\frak c$, no?
Jan
21
comment Proof correctness problem
@Marek: I don't want to get into a discussion which is over six months old. But let me say that expecting that seems to me equivalent to expecting miracle drugs that cure your sickness in minutes. Things just don't work that way.
Jan
21
comment Krein Milman theorem without the axiom of choice
Also, who is "M." Karagila?
Jan
21
comment Krein Milman theorem without the axiom of choice
Should I post it as an answer? Or maybe you should (I have to go now for a while)
Jan
21
comment Krein Milman theorem without the axiom of choice
Do you know this paper by Bell and Fremlin?
Jan
20
awarded  Nice Answer
Jan
19
comment Does k(X) have a k-basis for every set X, without AC?
Yes, there are different type of amorphous sets. It seems to me that you describe a strongly amorphous set, which is indeed the one from Fraenkel's first model (and being a strongly amorphous set does not characterize that model either, I know). Additionally, you seem to require that $A$ is not embeddable into $k$.
Jan
19
comment Does k(X) have a k-basis for every set X, without AC?
(1) I'll have to admit to have skipped over that part :-P (3) I don't see how, you took the first Fraenkel model, with the sets satisfying ZF and the addition hypothesis; there were no particular permutations or support structure chosen to ensure something, just the most basic example. (4) Well, the Cohen forcing is countable, so it admits all the choice-familiar structure (which include chain conditions and their consequences, choice function from dense sets, etc.) so it should work out just fine.
Jan
19
comment Does k(X) have a k-basis for every set X, without AC?
I don't even know what a symmetric basis (or an almost symmetric basis) is; but I do know that it was a strange move to go from $\sf ZF$ to $\sf ZFA$ back to $\sf ZF$. Especially since it seems to me that all you did was to add an amorphous set (which we can easily do using a Cohen forcing, so no appeals to choice are needed there).
Jan
18
accepted Sierpinski's construction of a non-measurable set