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bio website math.lsa.umich.edu/~ablass
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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 Dedekind-finite arithmetic vs natural numbers arithmetic
Apr
5
comment Are there any standard analysis facts that can be proven or arrived only by means of non-archimedean extensions of reals and non-standard 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 complex-analysis 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 now-deleted 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 teaching-based research
fixed typo
Apr
1
answered Historical (personal) examples of teaching-based 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 set-theorist'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 set-theoretic"? 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?