bio  website  math.lsa.umich.edu/~ablass 

location  US  
age  
visits  member for  4 years, 11 months 
seen  3 hours ago  
stats  profile views  11,660 
15h

comment 
“The Two Sheriffs” puzzle
@Yakky Not quite. The suspect eliminated by the lynch mob would have to also be eliminated by each of the sheriffs. 
Apr 10 
answered  Axiom of choice for sets of finite sets 
Apr 10 
awarded  Nice Answer 
Apr 10 
awarded  Nice Answer 
Apr 7 
answered  Dedekindfinite arithmetic vs natural numbers arithmetic 
Apr 5 
comment 
Are there any standard analysis facts that can be proven or arrived only by means of nonarchimedean extensions of reals and nonstandard analysis?
The new results about real analysis that are provided by complex analysis are not impossible to obtain in real analysis. You could take the complexanalysis proof and rewrite everything in terms of real numbers (real and imaginary parts) without ever mentioning complex numbers. Of course those proofs would be ugly, hard to find and hard to understand, but they would not be impossible. Similar comments apply to nonstandard analysis. 
Apr 4 
revised 
Does the countable $\sigma$product of a separable Hilbert space have a first countable topology?
fixed a typo 
Apr 4 
answered  Does the countable $\sigma$product of a separable Hilbert space have a first countable topology? 
Apr 4 
awarded  Good Answer 
Apr 2 
awarded  Disciplined 
Apr 2 
comment 
uncountable algebraically closed field other than C ?
As pointed out by Wesley Calvert in a nowdeleted answer, the algebraic closure of $\mathbb C(X)$ would work only in the weak sense that it's not identical with $\mathbb C$. It is isomorphic to $\mathbb C$ (provided the axiom of choice holds). 
Apr 2 
comment 
Philosophical arguments in defense (or against) large cardinals
The considerations described here make me fairly confident about the existence of indescribable cardinals. As I mentioned in my answer to the earlier question linked by the OP, that confidence does not extend even to subtle cardinals, because their definition seems to be not merely a matter of being "large" or "resembling the whole universe" but rather another sort of combinatorics for which I don't see a philosophical justification. 
Apr 1 
awarded  Nice Answer 
Apr 1 
revised 
Historical (personal) examples of teachingbased research
fixed typo 
Apr 1 
answered  Historical (personal) examples of teachingbased research 
Mar 31 
comment 
Projective family of probability spaces
Liviu is right. In a category of probability spaces, one wants morphisms that respect the whole probability space structure, not just the $\sigma$algebra but also the measure. 
Mar 31 
comment 
Antichain on $\mathcal{P}(\omega)/fin$ of cardinality $2^{\aleph_0}$?
It might be worth pointing out that this example works whether you use the settheorist's definition of antichain (pairwise incompatible) or everybody else's definition (pairwise incomparable). If you wanted only the latter, weaker sort of antichain, you could take the sets $\{k:r<q_k<r+1\}$ for all reals $r$. 
Mar 31 
comment 
Publication in proceedings
@SébastienPalcoux The word "Proceedings" in the title of a journal tells me nothing about the quality of the Journal. Proc. Amer. Math. Soc. is a high quality journal. (Full disclosure: Some years ago, I was on its editorial board.) Proc. Indian ... might also be a good journal, but I'd have to check; I never heard of it until just now, and that makes me a little suspicious. 
Mar 29 
awarded  Nice Answer 
Mar 27 
comment 
In set theory, is there a name for a function which maps the empty set to zero and all the others to one?
It's not clear what you want, as you've already defined $f$. Do you want a definition that "looks more settheoretic"? Do you want one that doesn't use a case distinction? Or what? One possible description of your $f$ is that $f(S)=$ the number of functions to the empty set from the set of functions to the empty set from $S$, i.e., $0^{0^{S}}$. Is this the sort of thing you were looking for? 