Andres Caicedo
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Registered User
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Set theorist.
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Jun 15 |
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Analysis of the boundary of the Mandelbrot set (It is a nice question, by the way.) |
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Jun 15 |
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Analysis of the boundary of the Mandelbrot set Is $\mathbb Z$ the complex plane? What does the $n$ stand for in your last line? Your symbols really don't seem to mean what you want them to mean. ($\ni$?) As a piece of general advice, symbols for their own sake just clutter the text, they are not really adding to the understanding of what you are trying to say. |
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Jun 15 |
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When 2^a = 2^b implies a=b (a,b cardinals) See also math.stackexchange.com/a/420484/462. |
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Jun 15 |
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Equality of Cardinality of Power Set See also math.stackexchange.com/a/420484/462 |
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Jun 13 |
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Nearly all math classes are lecture+problem set based; this seems particularly true at the graduate level. What are some concrete examples of techniques other than the “standard math class” used at the *Graduate* level? Very neat suggestion. |
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Jun 13 |
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What would remain of current mathematics without axiom of power set? @Andrej, in a different direction, we study definable inner models (such as $L$), effectively replacing the power set axiom by definable restrictions. |
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Jun 13 |
accepted | Coding a model of $0^\sharp$ from a $\Pi^1_1$ Gale-Stewart game |
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Jun 13 |
answered | Coding a model of $0^\sharp$ from a $\Pi^1_1$ Gale-Stewart game |
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Jun 10 |
awarded | ● Good Answer |
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Jun 8 |
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The Jones-Sato-Wada-Wiens polynomial for prime numbers and differential calculus ? The first of your bonus questions seems to me to be a bit lazy, surely unintentionally. The proof of the Jones-Sata-Wada-Wiens theorem tells you how to find the variables. |
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Jun 7 |
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the following inequality is true，but I can’t prove it (I've deleted an obsolete comment above. The link to the math.SE version is here: math.stackexchange.com/q/413558/462) |
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Jun 7 |
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the following inequality is true，but I can’t prove it Ah, you are right, thanks. |
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Jun 6 |
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The Jones-Sato-Wada-Wiens polynomial for prime numbers and differential calculus ? The term quid is looking for is r.e. (recursively enumerable), also called c.e. (computably enumerable). These are the sets of numbers that can be the output of a computer program running forever. |
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Jun 6 |
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Primes for which 2 and -2 are residues. This may be of interest: math.stackexchange.com/q/9648/462 |
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Jun 4 |
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The Erdős-Turán conjecture or the Erdős' conjecture? Why, indeed! Thanks. Hopefully he'll notice this question, he may have further comments to add. |
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Jun 4 |
awarded | ● Nice Answer |
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Jun 3 |
answered | The Erdős-Turán conjecture or the Erdős' conjecture? |
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Jun 2 |
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Rabin’s Tree Theorem added 447 characters in body |
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May 31 |
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Unpublished works of Woodin on SCH and Radin forcing (I've moved and expanded my comments to an answer.) |
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May 31 |
answered | Unpublished works of Woodin on SCH and Radin forcing |
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May 28 |
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The status of ‘the consistency of NF relative to ZF’ plus.google.com/103404025783539237119/posts/… Randall has a manuscript, that is still only being privately circulated while it is polished. If you email him directly, most likely he will email you a copy. |
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May 28 |
awarded | ● Nice Answer |
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May 26 |
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How many subsets of $\mathbb{R}$ are order isomorphic to $\mathbb{Q}$? (@HannaK. Yes, of course. Silly typo.) |
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May 26 |
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How many subsets of $\mathbb{R}$ are order isomorphic to $\mathbb{Q}$? There are $\mathfrak c$ subsets of $\mathbb R$ (and of $\omega_1\times[0,1)$) of size $\mathfrak c$, so really there is only one possibility. |
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May 21 |
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objects which can’t be defined without making choices but which end up independent of the choice On the other hand, the axiom of choice is needed to show that the dimension of a vector space is well-defined: Without choice, we could have spaces without bases, or with bases of different sizes. |
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May 20 |
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Square root of a positive $C^\infty$ function. See also the follow-up mat.univie.ac.at/~michor/roots2.pdf |
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May 19 |
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What are the main structure theorems on finitely generated commutative monoids? John, sorry, is your question the last sentence? |
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May 17 |
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Does this property of a partially ordered set have a name? For the last example in the post, see mathoverflow.net/questions/130768/… |
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May 16 |
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Cardinals without choice: interpolation (reference wanted) (Asaf: You may leave a comment at the beginning of the answer, indicating that the comments refer to a prior, completely different, version of the answer.) |
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May 15 |
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Cardinals without choice: interpolation (reference wanted) Funny, when you mentioned this in your previous question, I almost asked for a reference. I'm still in the process of trying to dig one up myself. (In other news, I believe Marion and I owe you an email.) |
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May 14 |
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What Are Some Naturally-Occurring High-Degree Polynomials? Thank you, John. (It would be nice if they digitized the book so others can see it.) |
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May 14 |
awarded | ● Yearling |
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May 11 |
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Counterintuitive consequences of the Axiom of Determinacy? For how a proof of item 3 can proceed, see math.stackexchange.com/questions/385630/… |
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May 11 |
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What Are Some Naturally-Occurring High-Degree Polynomials? @JohnStilwell I know this is an old comment, but could you please expand on it? I find this very interesting, and would be nice to mention something about it next time it comes up in lecture. (I know of no works criticizing Hermes's construction) |
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May 9 |
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What Are Some Naturally-Occurring High-Degree Polynomials? See also math.stackexchange.com/q/387062/462 |
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May 7 |
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Forcing mildly over a worldly cardinal. @Noah: In general that won't work: We could have $\theta$ measurable, and force it to become of cofinality $\omega$ without adding bounded subsets. Or we could already begin with $\theta$ of cofinality $\omega$, and then there is no cofinality change we can make. |
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May 6 |
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If ZFC has a transitive model, does it have one of arbitrary size? added 366 characters in body |
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May 6 |
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If ZFC has a transitive model, does it have one of arbitrary size? added 205 characters in body |
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May 6 |
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If ZFC has a transitive model, does it have one of arbitrary size? added 3033 characters in body |
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May 5 |
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If ZFC has a transitive model, does it have one of arbitrary size? Thanks, Joel. I figured Ali should have something on this question, and was planning to track down a reference. |
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May 5 |
answered | If ZFC has a transitive model, does it have one of arbitrary size? |
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May 5 |
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Classic applications of Baire category theorem Nice reference. Thanks! |
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May 5 |
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A question about “paradoxical” sentences in the language of ZF set theory. "$x$ has size $3$". "$x$ belongs to an even level of the cumulative hierarchy." |
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May 4 |
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How additive is Lebesgue measure in ZF+AD ? added 590 characters in body; added 81 characters in body; added 1 characters in body |
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May 1 |
answered | Basis theorem (due to Solovay?) |
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May 1 |
revised |
Counterintuitive consequences of the Axiom of Determinacy? added 754 characters in body |
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Apr 30 |
awarded | ● Nice Answer |
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Apr 30 |
revised |
Counterintuitive consequences of the Axiom of Determinacy? added 1829 characters in body |
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Apr 29 |
revised |
Counterintuitive consequences of the Axiom of Determinacy? added 44 characters in body |
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Apr 29 |
revised |
Counterintuitive consequences of the Axiom of Determinacy? added 462 characters in body |
