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33790
bio website boolesrings.org/asafk
location Israel
age 29
visits member for 4 years, 2 months
seen 1 min ago

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


3h
comment Paritial order help?
Please don't ask that on Math.SE. It has been asked like five times by now. Talk to your classmates instead.
22h
revised Defining a topology in the Power Set
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1d
comment Exponentiation and Dedekind-finite cardinals
[...] For example, list all the names in the ground model, and then map each name into a pair of countable ordinals $(\alpha,\beta)$, such that there is an antichain interpreting the name as an actual symmetric name, and then mapping it into \beta. You can do that, then choose equivalence classes under orbits of permutations (which move finitely many reals anyway) and create a name which is stable under automorphisms. By counting arguments you don't go above $\omega_1$ names, so everything is just peachy.
1d
comment Exponentiation and Dedekind-finite cardinals
Andres, here is a sketch, and you can tell me what's wrong with it. Let $\dot A$ be the name of the generic D-finite set. Then there is a name (for the full extension) of an injection from $2^A$ into $2^\omega$, since in the full Cohen model, $A$ is countable. Now consider a list in the ground model of all the names of subsets of $A$. Since the forcing is ccc, there are only continuum many, so we there are only continuum many symmetric ones (externally). Now by usual arguments build a name which $1$ forces to be an injection from all these sets into $\omega_1$. [...]
1d
revised Exponentiation and Dedekind-finite cardinals
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1d
comment Exponentiation and Dedekind-finite cardinals
Yeah, that is also true. I'll give it some thought, I'm sure there's a quick argument.
1d
comment Exponentiation and Dedekind-finite cardinals
Andres, in the Cohen model, I believe the power set of the Dedekind finite set of reals should be equal to the reals. It is certainly as big. I'll have to think about an argument for the other direction, but I'm sure it's true.
1d
answered Exponentiation and Dedekind-finite cardinals
2d
awarded  Nice Question
2d
comment Is there a “hereditary” construction for $L$?
@Mohammad: Sure! Thanks for thinking this question over! :-)
2d
comment Which axioms of ZF are used for finite choice?
@Joel: Perks of having a gold badge in the tag, you get a supervote about closing and reopening duplicates.
2d
comment Which axioms of ZF are used for finite choice?
@Joel: But that's a big "provided". Since one can easily manufacture a model where this fails using compactness. Of course the failure is at non-standard finiteness, but still it makes finite choice unprovable (internally).
2d
revised Which forcing types preserve the axiom of determinacy?
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2d
comment Which forcing types preserve the axiom of determinacy?
Alright then, your point is a good one. Let me rule that option out.
2d
comment Which axioms of ZF are used for finite choice?
Since we use induction to prove finite choice, we need to somehow disallow induction. I suppose disallowing sufficiently many replacement/separation axioms will do the trick. But when you remove these axioms you really just get left with a very weak theory, not something I would call "set theory" in any serious meaning of the term.
2d
comment Which forcing types preserve the axiom of determinacy?
@Joel: Subset of $\mathcal P(\Bbb R)$. Since we can think of $\Bbb R$ as $\mathcal P(\omega)$, adding a real, a set of reals, or a set of sets of reals are all included in this definition. But both interpretations are interesting anyway. :-)
2d
asked Which forcing types preserve the axiom of determinacy?
Aug
24
reviewed Close How to solve the definite integral?
Aug
22
reviewed Reviewed concepts in fields other than physics and computer science which touch on concepts that are fundamental in pure mathematics
Aug
22
comment concepts in fields other than physics and computer science which touch on concepts that are fundamental in pure mathematics
Held back? This is why mathematics can bloom into its abstract beauty! Things which have "real world applications" tend to end up being bogged with ugly details. Especially when mathematics in its nature is not empirical like biology and physics (yes yes, I know that in mathematics you do have an "empirical" testing when you verify theorems on known objects or whatever, this is not what I meant, obviously).