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Dec
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comment How can I prove that the additive group of rationals is not isomorphic to a direct product of two nontrivial groups?
Here is an approach: show that any two nontrivial subgroups of $\mathbb{Q}$ have nontrivial intersection. Seems very localized though, I would like to see a more general argument.
Oct
28
comment Properties of computable numbers
There is no effective enumeration of all computable numbers. However, there are effective enumerations of the Turing machines, but not all Turing machines compute real numbers. How should we think of those machines that don't compute real numbers?
Sep
5
revised What's the difference between these two Venn diagrams?
spelling in title
Sep
5
suggested approved edit on What's the difference between these two Venn diagrams?
Sep
1
revised Descriptions of sets and the Axiom of Choice
correction
Aug
31
comment Descriptions of sets and the Axiom of Choice
Well, $OD$ is transitive whenever $V = OD$ since $V$ is always transitive, so $V = OD$ and $V = HOD$ mean exactly the same thing.
Aug
31
answered Descriptions of sets and the Axiom of Choice
Aug
27
answered Formalizing metamathematics
Aug
23
comment Can one avoid AC in the proof that in Noetherian rings there is a maximal element for each set?
Good point, Arturo. Note that Hodges separates the three definitions in the paper cited above.
Aug
22
comment Karatsuba vs. Schönhage-Strassen for multiplication of polynomials
This answer assumes that the coefficients of the polynomials are integers. I thought that was part of the question, but I now see that it wasn't...
Aug
22
revised Karatsuba vs. Schönhage-Strassen for multiplication of polynomials
small correction
Aug
22
comment Can one avoid AC in the proof that in Noetherian rings there is a maximal element for each set?
Yes, see W. Hodges, Six impossible rings, J. Algebra 31 (1974), 218-244.
Aug
22
answered Can one avoid AC in the proof that in Noetherian rings there is a maximal element for each set?
Aug
22
revised Karatsuba vs. Schönhage-Strassen for multiplication of polynomials
fixed typo
Aug
22
answered Karatsuba vs. Schönhage-Strassen for multiplication of polynomials
Aug
9
comment For every infinite $S$, $|S|=|S\times S|$ implies the Axiom of choice
@Asaf: I'm not used to the quality standards of this site, if you (or anyone else) want to flesh out my answer, please go right ahead...
Aug
9
revised For every infinite $S$, $|S|=|S\times S|$ implies the Axiom of choice
rewording