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Apr
17
revised When are unions of isomorphic groups isomorphic?
deleted 1 character in body
Apr
17
comment When are unions of isomorphic groups isomorphic?
I believe one can get by with less. We simply need the homomorphisms $H_i \rightarrow G_j$ to agree on any particular element of $H$ for $i$ sufficiently large in the sense if the directed index set $I$. But then the graph of the desired homomorphism will emerge from an intersection of unions.
Apr
17
revised When are unions of isomorphic groups isomorphic?
Correction hopefully to obtain the intended meaning, seeing as $G_i and G_j$ are not generally isomorphic.
Apr
7
accepted Limits of rearranged sequences along ultrafilters
Apr
7
revised The paradox with the first uncountable ordinal
Fixed TeX error
Apr
7
revised The paradox with the first uncountable ordinal
Fixed wording
Apr
7
revised Cofinality of countable ordinals in ZF, and in toposes
added 1 character in body
Apr
7
asked Cofinality of countable ordinals in ZF, and in toposes
Apr
6
revised Limits of rearranged sequences along ultrafilters
added 70 characters in body
Apr
6
comment Limits of rearranged sequences along ultrafilters
@Paul McKenney. You're correct, of course. Fixed.
Apr
6
asked Limits of rearranged sequences along ultrafilters
Mar
29
comment Paradoxical spherical caps
@Wojowu Look at the final slide, which contains this theorem: For all $n \geq 2$, any two subsets of $S^n$, each of which has nonempty interior, are $SO (n + 1)$ equidecomposable. In particular, $S^n$ is equidecomposable with every subset of it whose interior is nonempty.
Mar
25
revised Paradoxical spherical caps
edited tags
Mar
25
revised Equations for covering spaces of non-singular curves
edited tags
Mar
24
comment Equations for covering spaces of non-singular curves
Thank you Alexandre! I have a question though. After a projection or two, my $C$ comes to you explicitly as a branched cover of the Riemann sphere, and thus also $C'$. What's the theoretical advantage of first approximating, then finding a model of $C$ and then $C'$ branched over $0,1 \infty$, thus throwing away the original branching data?
Mar
24
asked Equations for covering spaces of non-singular curves
Mar
22
asked Paradoxical spherical caps
Mar
14
comment Succinctly naming big numbers: ZFC versus Busy-Beaver
I see no philosophical obstacle to conversing informally about the standard natural numbers, so I'm with Scott on that. That said, when some conjecture emerges, interlocutors need to agree about what sort of discourse could settle it. But naive informal logic leads to paradoxes; first-order logic can't see the standard natural numbers; and full second-order number theory doesn't come with universally accepted laws of deduction. I agree with Scott's critics that (while one can ask these questions informally) any attack must begin with an as yet undetermined formalization.
Mar
6
comment Local differential geometry and invariant theory
Based on Robert Bryant's answer (thank you!) I found this old question mathoverflow.net/questions/109669/curvature-as-metric-invariant where Peter Michor recommends his own book: See section 33 of the book: Ivan Kolár, Jan Slovák, Peter W. Michor: Natural operations in differential geometry. Springer-Verlag, Berlin, Heidelberg, New York, (1993), (pdf).
Mar
6
accepted Local differential geometry and invariant theory