bio | website | jdh.hamkins.org |
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location | New York City | |
age | ||
visits | member for | 5 years, 7 months |
seen | 1 hour ago | |
stats | profile views | 54,389 |
I am professor of mathematics, philosophy and computer science at the City University of New York (CUNY Graduate Center & College of Staten Island). Currently I am visiting at New York University.
My research is mostly in logic, broadly construed, especially mathematical logic and set theory, with connections to other areas.
Find out more on my blog: mathematics and philosophy of the infinite
Jun 27 |
awarded | Notable Question |
Jun 26 |
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What is the significance of having Prime Ideal Theorem in models for failure of Axiom of Choice?
Well, it seems more like asking what are the issues about having only PIT instead of AC. I think that many mathematicians would appreciate a well-thought-out summary answer to that. |
Jun 26 |
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What is the significance of having Prime Ideal Theorem in models for failure of Axiom of Choice?
This question is on-topic here at MO. @Asaf, why not just answer it? |
Jun 26 |
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Optimal strategy for game of 'online sorting' into a poset
Nice question! Do you know a demonstrably optimal solution in the case where the poset is a linear order? |
Jun 25 |
awarded | Nice Answer |
Jun 25 |
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Prove bijection beetween sets
Probably you intend to ask for a bijection from $X\setminus Y\to X$, rather than what you wrote. (Note also that the desired implication will need the axiom of choice, since it is false when $X$ is an infinite Dedekind-finite set.) |
Jun 24 |
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Example of a collection of metacompact spaces with non-metacompact box-product
Do you know whether $\mathbb{R}^\omega$ is metacompact in the box topology? Or $\prod_{n\in\omega}[0,1]$? |
Jun 24 |
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Where to buy premium white chalk in the U.S., like they have at RIMS?
Here is an interview with the company founder about why he has now regretfully closed the company: asia.nikkei.com/Business/Companies/… |
Jun 22 |
awarded | Nice Answer |
Jun 22 |
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Pseudo-decision procedures for first order arithmetic
For any theory in which one believes, say, ZFC plus large cardinals or whatever, then one can search for short proofs of arithmetic statements, saying "true" only when such is found; and saying "false" if a proof of the negation is found or if one has exceeded a fixed time bound. This algorithm does not depend on the quantifier complexity of the given statement, but only on the length of the proof and whether it is shorter than the pre-fixed bound. |
Jun 22 |
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Pseudo-decision procedures for first order arithmetic
Even the halting problem itself is coarsely decidable in linear time -- see mathoverflow.net/a/58074/1946. |
Jun 20 |
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$\mathbb{P}_{\kappa}$ forces non$(\mathcal{M})$=cov$(\mathcal{M})=\kappa$
In the definition of $\mathbb{E}$, do you mean $s\in \omega^{<\omega}$ rather than $s\in \omega^\omega$? |
Jun 17 |
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Proof of a soft version of Moschovakis's lemma
The proof is basically like you say, except that it is also combined with an induction of surjections onto $P(\beta)$ for $\beta<\alpha$. You play a game where player I tries to play a real coding an initial segment of the image of $X$ (using the earlier surjections), and player II tries to play a longer initial segment. It is then not difficult to show that if $X\neq Y$ then no winning strategy in $G(X)$ is winning in $G(Y)$. |
Jun 17 |
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Countable group with uncountable number of subgroups $< 2^{\aleph_0}$
Emil, why not post as an answer? Although the set theorists are accustomed to thinking of the class of countable groups as a Polish space, this might be less familiar to the group theorists, and so this may be a good opportunity to explain this perspective. |
Jun 17 |
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Non-standard naturals and goodstein sequences
Since Goodstein's theorem is true in the standard model, all Goodstein sequences terminate in the standard model. The independence result provides nonstandard models in which there are Goodstein sequences that don't terminate. (But meanwhile, there are also nonstandard models of true arithmetic, so it is also true that there are nonstandard models where all Goodstein sequences terminate.) |
Jun 13 |
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Set theory identity, can't derive it
The problem may arise from an order-of-operations issue in you original expression. You seem to assume that the minus sign $-E$ is applying only to $(C-D)$ and not to $A\cup(C-D)$. So your parentheses are off in your calculation because of this issue. |
Jun 13 |
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Set theory identity, can't derive it
Your question will be a better fit at math.stackexchange.com, and so I have voted to migrate it there. |
Jun 12 |
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Saturation of null ideal
Yes, I just came to a similar conclusion myself... |
Jun 12 |
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Saturation of null ideal
You have it already as a consistency assertion? |
Jun 12 |
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Just a little absoluteness might be cheaper?
Also, even if $\mathbb{P}$ was literally the same poset in $L$ and the extension by $L$ of $\mathbb{P}$, if it wasn't homogeneous, then one can make the poset do totally different things under different conditions. |