François G. Dorais
Reputation
117/100 score
 2d comment Can we recover a topological space from the collection of Borel probability measures living on it? To add one more to the comments already present. If you take any topological space $X$ and a Borel set $B$ which is not open, form $X'$ by extending the topology of $X$ in such a way that $B$ is open in $X'$. Then $X$ and $X'$ have the same Borel algebra but different topologies. Oct 3 revised Intuition behind salient numbers in number of h-cobordism classes of smooth homotopy n-spheres rolled back to a previous revision Oct 2 revised Nelson's program to show inconsistency of ZF second manuscript Oct 1 awarded Nice Answer Oct 1 revised Nelson's program to show inconsistency of ZF update Sep 27 comment Two strengthenings of “strong measure zero” I don't think you want $Eps$ to be topologized as usual. It would be more interesting to use Baire space instead of $Eps$ and let $f \in \omega^\omega$ correspond to the sequence $\epsilon_n = 2^{-f(n)}$, for example. The issue is that $Eps = (0,\infty)^\omega$ is connected. If $x \in X$ and $X$ is csmz via $F$, we can define $H_x:Eps \to \omega$ by $H_x(f) = \mu n[x \in F(f)(n)]$. Since $\omega$ is discrete and $H_x$ is continuous, $H_x$ must be constant. If $x \neq y$, then $H_x$ and $H_y$ can't have the same constant value and it follows immediately that $X$ is countable. Sep 24 comment Relative null-ness The bibliography would also be a great answer! Sep 24 comment Surreal compactness @Joel, I'm wondering too. I thought your example could be coerced into a counterexample for a set-sized union of open classes but that's not obvious. Sep 24 revised Surreal compactness fixed typo and confusing terminology Sep 24 answered Surreal compactness Sep 18 comment Is there a sigma algebra without atoms on a countably infinite set ? Hi Mirna, unfortunately I'm drawing a blank on what I was thinking when I wrote this in 2010. I wish I had included the reference in the post. I'm digging through some old stuff in the hope of jolting my memory. I will let you know if I find anything. Sep 16 comment How far wrong could the Continuum Hypothesis be? I think this is a serious gap in Wikipedia. Systematic failures of GCH are interesting (and require extremely high-level machinery) but, as far as $2^{\aleph_0}$ is concerned, the answer has been known since soon after Cohen! Basically, the only restriction is provided by König's Theorem that $\operatorname{cf}(2^{\aleph_0}) > \omega$. Sep 13 awarded Necromancer Sep 13 comment Does Arzelà-Ascoli require choice? Andres, I gather you're in Ann Arbor now. Do you think there is a chance to stabilize this wonderful resource in the near future? Sep 13 answered Nelson's program to show inconsistency of ZF Sep 8 comment The least admissible above a dominating real For the benefit of those who haven't read Blass's paper, he shows that the (1) every hyperarithmetic real is computable in every Hechler generic and (2) the only reals that are computable in every Hechler generic are the hyperarithmetic reals. Sep 8 comment The least admissible above a dominating real Blass addresses a different question but the paper does have the right tools and references. What you're asking is significantly harder, as far as I know. Maybe you'll also need something like the Baumgartner-Dordal analysis of Hechler forcing to get the right density arguments. Sep 8 comment The least admissible above a dominating real This is not easy to work through. You need some classic results of Solovay and Jockusch on "introreducibility". See Andreas Blass's paper Needed Reals and Recursion in Generic Reals [APAL 109 (2001), 77-88]. Sep 6 comment Equational theories determined by “identities without variables” I'm happy to see this question come back after so long! My initial suggestion was clearly flawed as others have pointed out. I'm curious again! Sep 3 revised Logically independent but true sentences typo