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  • 0 posts edited
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  • 74 votes cast
Apr
24
asked Nonexistence of generic objects over $L(\mathbb{R})$
Mar
8
comment Is the set of subsequences of branches through a tree Borel?
Thanks Joel. While I don't need it at the moment, it might be nice to have a sketch of the argument for why the set can be complete analytic in the not-necessarily increasing case.
Mar
8
accepted Is the set of subsequences of branches through a tree Borel?
Mar
8
asked Is the set of subsequences of branches through a tree Borel?
Feb
26
awarded  Nice Question
Nov
29
comment An interpretation for filters of subspaces in Banach spaces
Yep, in fact, those results are exaclty the reason I posed the question. I'm particularly looking for interpretations in other spaces, like $\ell^p$ and $c_0$.
Nov
28
asked An interpretation for filters of subspaces in Banach spaces
Nov
23
revised A property of uncountable almost disjoint families
Added parenthetical comment to Q2.
Nov
23
awarded  Yearling
Nov
23
revised A property of uncountable almost disjoint families
edited body
Nov
23
revised A property of uncountable almost disjoint families
Added "Question 2".
Nov
23
revised A property of uncountable almost disjoint families
Added note "EDIT"
Nov
23
accepted A property of uncountable almost disjoint families
Nov
23
comment A property of uncountable almost disjoint families
@FedorPetrov I had a related application in mind, and this is all that was necessary. Certainly a witness in $\mathcal{A}$ would be fine.
Nov
23
asked A property of uncountable almost disjoint families
Aug
27
comment When do block sequences yield disjoint subspaces?
Bill: I'm a bit unfamiliar with the terminology (Banach space theory is a outside my usual area), what do you mean by "minimal sequence" and "M-basis"?
Aug
24
asked When do block sequences yield disjoint subspaces?
May
20
accepted When is a filter generated by a (countable) chain?
Apr
20
accepted Existence of state on a C*-algebra satisfying $|\tau(ab)|=\|ab\|$
Apr
20
comment Classification of complex structures on $\mathbb{R}^{2n}$
This paper of Hjorth and Kechris may be of interest: projecteuclid.org/euclid.ijm/1255984956. It deals with using descriptive set theory to understand the classification problem for arbitrary Riemann surfaces (not just structures on $\mathbb{R}^{2n}$), and shows that even in complex dimension $1$, this is extremely complicated (the "moduli space" is "Borel equivalent" to the quotient of $\{0,1\}^{F_2}$ by the left shift action of the free group $F_2$). For higher dimensions, it is more complicated ("not classifiable by countable structure" in the subject's parlance).