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comment Borel coloring of a graph on the set of all functions $f:\mathbb{N}\to\mathbb{N}$
Since you mentioned absoluteness of the property that a real codes a Borel coloring, it seems appropriate to mention that you also use, at the end of the proof, the absoluteness of the property that changing one value of a function changes its color.
May
11
comment Formulating Kunen's inconsistency and Reinhardt cardinals in term of category theory
A special case of your item 4 is the topic of: Adelman, Murray(5-MCQR); Blass, Andreas(1-MI) Exact functors, local connectedness and measurable cardinals. (Italian summary) Rend. Sem. Mat. Fis. Milano 54 (1984), 9–28 (1987).
May
11
comment Formulating Kunen's inconsistency and Reinhardt cardinals in term of category theory
Thanks for citing my paper, but, to give proper credit, I must point out that the main results were discovered earlier by Trnkova and Reiterman. See: Corrections to: “Exact functors and measurable cardinals” Pacific J. Math. 73 (1977), no. 2, 540.
May
10
comment Formulating Kunen's inconsistency and Reinhardt cardinals in term of category theory
@JoelDavidHamkins Thanks for the clarification. If I remember correctly, global choice was in both Kelley's and Morse's axiomatizations, but it was also in Gödel's version of GB (Axiom E, I think); I'm not sure about Bernays, but von Neumann had it in the form "all proper classes are in bijection with V". So it seems the presence of choice in a system named after someone need not agree with its presence in that person's axioms. (That's certainly the case for Zermelo and ZF.)
May
10
comment Formulating Kunen's inconsistency and Reinhardt cardinals in term of category theory
@JoelDavidHamkins I never realized that KM and GB differ in regard to global choice. I thought the difference between them was just whether the class comprehension axioms allow quantification of class variables, and that the presence or absence of global choice was an orthogonal issue.
May
9
comment Which operators other than self-adjoint operators have no purely imaginary eigenvalues?
Don't you want $A^4-I$ to be nonsingular? Otherwise, $A$ could have some eigenvalues at $\pm i$ and others off the imaginary axis, whereas the question wants all the eignevalues off the imaginary axis.
Apr
29
comment Reverse mathematics of (co)homology?
Concerning the need for the axiom of choice in setting up homological machinery, you might want to also look at another paper of mine (in addition to the one Francois cited): "Injectivity, projectivity, and the axiom of choice" [Trans. A.M.S. 255 (1979) 225-240].
Apr
28
awarded  Enlightened
Apr
28
awarded  Nice Answer
Apr
28
answered What defines a “short proof”?
Apr
25
awarded  Enlightened
Apr
25
awarded  Nice Answer
Apr
24
awarded  Yearling
Apr
23
comment How seriously should a graduate student take teaching evaluations?
I wouldn't recommend listing the evaluation numbers when they're good and omitting them when they're bad. If I were evaluating a candidate whose teaching record is presented as in this answer, I'd infer that the one number on the list was a particularly good one, and I'd wonder how bad the omitted numbers are. I recommend providing all or none of your teaching evaluation numbers.
Apr
22
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?
@Anixx Your comment is correct as long as one doesn't distinguish between provability and truth. If one does make such a distinction, though, then arithmetic is weaker than set theory, but real analysis is not weaker than complex analysis.
Apr
22
comment Lebesgue covering dimension for locales
You presumably meant to say also that $D$ should be a refinement of $C$.
Apr
21
comment What are the most misleading alternate definitions in taught mathematics?
@AllenKnutson I like "ichthyomorphism"; is it your invention? Google finds only a few occurrences of this word, and the only one that looks mathematical is this MO page.
Apr
20
answered Illfounded trees as “retract” of all trees
Apr
18
awarded  Necromancer
Apr
17
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.