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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This is a very interesting question (and I really want to see what other answers you receive). I do not know of any general metatheorems ensuring that what you ask (in particular, about consistency strength) is the case, at least under reasonable conditions. However, arguments establishing the proof theoretic ordinal of a theory $T$ usually entail this. You […]

This is false; take a look at https://en.wikipedia.org/wiki/Analytic_set for a quick introduction. For details, look at Kechris's book on Classical Descriptive Set Theory. There you will find also some information on the history of this result, how it was originally thought to be true, and how the discovery of counterexamples led to the creation of desc […]

This is open. In $L(\mathbb R)$ the answer is yes. Hugh has several proofs of this, and it remains one of the few unpublished results in the area. The latest version of the statement (that I know of) is the claim in your parenthetical remark at the end. This gives determinacy in $L(\mathbb R)$ using, for example, a reflection argument. (I mentioned this a wh […]

A classical reference is Hypothèse du Continu by Waclaw Sierpiński (1934), available through the Virtual Library of Science as part of the series Mathematical Monographs of the Institute of Mathematics of the Polish Academy of Sciences. Sierpiński discusses equivalences and consequences. The statements covered include examples from set theory, combinatorics, […]

There is a new journal of the European Mathematical Society that seems perfect for these articles: EMS Surveys in Mathematical Sciences. The description at the link reads: The EMS Surveys in Mathematical Sciences is dedicated to publishing authoritative surveys and high-level expositions in all areas of mathematical sciences. It is a peer-reviewed periodical […]

You may be interested in the following paper: Lorenz Halbeisen, and Norbert Hungerbühler. The cardinality of Hamel bases of Banach spaces, East-West Journal of Mathematics, 2, (2000) 153-159. There, Lorenz and Norbert prove a few results about the size of Hamel bases of arbitrary infinite dimensional Banach spaces. In particular, they show: Lemma 3.4. If $K\ […]

You just need to show that $\sum_{\alpha\in F}\alpha^k=0$ for $k=0,1,\dots,q-2$. This is clear for $k=0$ (understanding $0^0$ as $1$). But $\alpha^q-\alpha=0$ for all $\alpha$ so $\alpha^{q-1}-1=0$ for all $\alpha\ne0$, and the result follows from the Newton identities.

Nice question. Let me first point out that the Riemann Hypothesis and $\mathsf{P}$-vs-$\mathsf{NP}$ are much simpler than $\Pi^1_2$: The former is $\Pi^0_1$, see this MO question, and the assertion that $\mathsf{P}=\mathsf{NP}$ is a $\Pi^0_2$ statement ("for every code for a machine of such and such kind there is a code for a machine of such other kind […]

For brevity's sake, say that a theory $T$ is nice if $T$ is a consistent theory that can interpret Peano Arithmetic and admits a recursively enumerable set of axioms. For any such $T$, the statement "$T$ is consistent" can be coded as an arithmetic statement (saying that no number codes a proof of a contradiction from the axioms of $T$). What […]

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).

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