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Apr
12
comment Find the Flaw in the Argument
I suppose one flaw in the argument is using "the inequality in the hypothesis" when there is no inequality in sight.
Apr
9
comment $\aleph$ looks like $\mathbb N$?
@AsafKaragila Have you seen the MathSciNet review of the second edition of Bourbaki's set theory (MR0154814)? The last sentence reads: "In the first edition, all alephs except those appearing in exponents were printed upside down; in the new edition the exception has been removed."
Apr
8
comment Projectives and Injectives in Functor Categories
I believe this sort of thing was done by Charles Watts in "A homology theory for small categories" [Proc. Conf. Categorical Algebra, La Jolla; Springer (1966) 331-335]. I don't remember the details, nor do I have the paper handy, but the MathSciNet review sounds as though this paper may be relevant.
Apr
8
awarded  Enlightened
Apr
8
awarded  Nice Answer
Apr
4
comment regularity of ultrafilters
According to the MathSciNet review of Dieter Donder's paper "Regularity of ultrafilters and the core model" [Israel J. Math. 63 (1988) 289-322] all uniform ultrafilters on $\kappa$ are $(\omega,\kappa)$-regular provided there is no inner model with a measurable cardinal and the core model computes $\kappa^+$ correctly. (Presumably this refers to the original Jensen-Dodd core model.) So it seems we're OK with room to spare if $V=L$.
Apr
4
comment regularity of ultrafilters
Oops. I found the Prikry reference, "On a problem of Gillman and Keisler" [Ann. Math. Logic 2 (1970) 179-187], but according to the review on MathSciNet, it only proves the case $\kappa=\aleph_1$.
Apr
4
comment regularity of ultrafilters
I think Prikry proved that if $V=L$ then every uniform ultrafilter on any infinite $\kappa$ is $(\omega,\kappa)$-regular.
Apr
4
comment Given a set of generators of a group G, is there a method to find a presentation for G using those generators?
Start with your known presentation of $G$. Express each of $x$ and $y$ as terms built from those generators. Adjoin to your known presentation the two generators $x$ and $y$, and adjoin to the known relations the two equations that express $x$ and $y$ in terms of the original generators.
Mar
28
answered practical algorithms for np complete problems
Mar
27
comment Symmetry on a sphere
@AlexDegtyarev Edgar's comment was not about the area of the empty set. It was about the area of every one of the components, and the empty set is not a component. Since there are no components when $u$ is constant, what he wrote about all their areas is vacuously true.
Mar
26
comment ideals in the disk algebra
@AlexDegtyarev The current version of the question asks that the function be holomorphic in the interior.
Mar
24
revised what's the limit of cardinals can be proved to exist in ZFC
fixed a typo
Mar
24
answered what's the limit of cardinals can be proved to exist in ZFC
Mar
18
comment Is a model of arithmetic contained in a model of arithmetic an initial segment?
In the 1950's, MacDowell and Specker proved that every model of PA has an elementary end extension. Their method has become rather standard by now, but at the time this was a definitely nontrivial result.
Mar
13
answered Origin of exact sequences
Mar
12
awarded  Nice Answer
Mar
2
comment Function Approximation in c.c.c Forcings without AC in Ground Model
@AsafKaragila Right; Ccc for a poset is, as far as I can see, weaker than ccc for its Boolean completion.
Mar
2
comment Function Approximation in c.c.c Forcings without AC in Ground Model
Concerning the complete Boolean algebra case in the last paragraph of your answer, the situation is even better. If $P$ is a complete Boolean algebra and satisfies the c.c.c., then $F(a)$ will be countable because the truth values $\Vert \dot f(\check a)=\check b\Vert$ constitute an antichain.
Mar
2
comment Function Approximation in c.c.c Forcings without AC in Ground Model
I'm also accustomed to calling it the maximality principle.