So, we went to Kathryn Albertson Park, to play football. But it was so hot, and there were so many geese mementos on the grass, that Francisco felt unhappy, and wanted to go home instead.

We are walking back to the car, when

“Wait. Is that a Dalek?” Francisco was ahead of me. He stopped, came back, and looked at where the camera and I were pointing.

“Yes. That’s a Dalek. And that’s the Doctor.”

The part that I wasn’t expecting was what happened next. He looked at Najuma and I, scared, and said:

“I want to get in the car. Let’s go home.” He started to go for the car, then he looked at me. Why are you not running, you fool?

“No, wait, let me take another picture.”

“No, no, let’s go. Let’s go…” There is a Dalek in the park coming for us, you people, what are you doing? Run! RUN!!

“Oh, it’s talking, what is it saying?”

What else, really? EX-TER-…

So, yeah. We got in the car and sped out of there and into safety.

“Is the Dalek following us, papi?”

“No, I don’t think it is.”

“Are we safe at home?”

“Sure we are. And anyway, let me tell you, I’ll protect you of any Dalek attacks we may suffer, ok?”

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Yes. This is a consequence of the Davis-Matiyasevich-Putnam-Robinson work on Hilbert's 10th problem, and some standard number theory. A number of papers have details of the $\Pi^0_1$ sentence. To begin with, take a look at the relevant paper in Mathematical developments arising from Hilbert's problems (Proc. Sympos. Pure Math., Northern Illinois Un […]

I am looking for references discussing two inequalities that come up in the study of the dynamics of Newton's method on real-valued polynomials (in one variable). The inequalities are fairly different, but it seems to make sense to ask about both of them in the same post. Most of the details below are fairly elementary, they are mostly included for comp […]

Let $C$ be the standard Cantor middle-third set. As a consequence of the Baire category theorem, there are numbers $r$ such that $C+r$ consists solely of irrational numbers, see here. What would be an explicit example of a number $r$ with this property? Short of an explicit example, are there any references addressing this question? A natural approach would […]

Not necessarily. That $\mathfrak m$ is consistently singular is proved in MR0947850 (89m:03045) Kunen, Kenneth. Where $\mathsf{MA}$ first fails. J. Symbolic Logic 53(2), (1988), 429–433. There, Ken shows that $\mathfrak{m}$ can be singular of cofinality $\omega_1$. (Both links above are behind paywalls.)

Ignas: It is not possible to provide an explicit expression for a non-linear solution. The reason is that (it is a folklore result that) an additive $f:{\mathbb R}\to{\mathbb R}$ is linear iff it is measurable. (This result can be found in a variety of places, it is a standard exercise in measure theory books. As of this writing, there is a short proof here. […]

Following Tomas's suggestion, I am posting this as an answer: I encountered this problem while directing a Master's thesis two years ago, and again (in a different setting) with another thesis last year. I seem to recall that I somehow got to this while reading slides of a talk by Paul Pollack. Anyway, I like to deduce the results asked in the prob […]

This is a beautiful and truly fundamental result, and so there are several good quality presentations. Try MR1321144. Kanamori, Akihiro. The higher infinite. Large cardinals in set theory from their beginnings. Perspectives in Mathematical Logic. Springer-Verlag, Berlin, 1994. xxiv+536 pp. ISBN: 3-540-57071-3, or any of the newer editions (the 2003 second ed […]

Given any field automorphism of $\mathbb C$, the rational numbers are fixed. In fact, any number that is explicitly definable in $\mathbb C$ (in the first order language of fields) is fixed. (Actually, this means that we can only ensure that the rationals are fixed, I expand on this below.) Any construction of a wild automorphism uses the axiom of choice. Se […]

The Milner-Rado paradox is only a paradox in the traditional sense of the word: there are no inconsistencies here, but rather the result is (perhaps naively) seen as counter-intuitive. There are two reasons here: First, if $\alpha=\bigcup_{n

The question immediately reminded me of this. Here is an argument following the same basic idea at the beginning of that argument: First, consider $B=\{x\in A\mid A\cap(-\infty,x]$ is countable$\}$, and note that $B$ itself is countable: The point is that if $x\in B$ then $A\cap(-\infty,x]\subseteq B$. Now, if $B\ne\emptyset$, let $t=\sup B$, fix an increasi […]

RT @AoDespair: A free Wire boxed set signed by Idris Elba and Michael K. Williams to any unfaithful Elector. And the first round on me. #de… 3 days ago

I PLEDGED NOT TO EXTERMINATE TODAY!

Oh, how fantastic! And through Dalek Klaus’s twitter account, I found https://www.facebook.com/media/set/?set=a.10151472718672638.1073741852.95835192637&type=3&l=6282565f58 (148 pictures of the adventure).

[…] last year. See also here and […]

[…] Maybe they are chasing me, see here. […]