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?”

43.614000-116.202000

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(As I pointed out in a comment) yes, partial Woodinness is common in arguments in inner model theory. Accordingly, you obtain determinacy results addressing specific pointclasses (typically, well beyond projective). To illustrate this, let me "randomly" highlight two examples: See here for $\Sigma^1_2$-Woodin cardinals and, more generally, the noti […]

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Yes. Consider, for instance, Conway's base 13 function $c$, or any function that is everywhere discontinuous and has range $\mathbb R$ in every interval. Pick continuous bijections $f_n:\mathbb R\to(-1/n,1/n)$ for $n\in\mathbb N^+$. Pick a strictly decreasing sequence $(x_n)_{n\ge1}$ converging to $0$. Define $f$ by setting $f(x)=0$ if $x=0$ or $\pm x_n […]

All proofs of the Bernstein-Cantor-Schroeder theorem that I know either directly or with very little work produce an explicit bijection from any given pair of injections. There is an obvious injection from $[0,1]$ to $C[0,1]$ mapping each $t$ to the function constantly equal to $t$, so the question reduces to finding an explicit injection from $C[0,1]$ to $[ […]

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"There are" examples of discontinuous homomorphisms between Banach algebras. However, the quotes are there because the question is independent of the usual axioms of set theory. I quote from the introduction to W. Hugh Woodin, "A discontinuous homomorphism from $C(X)$ without CH", J. London Math. Soc. (2) 48 (1993), no. 2, 299-315, MR1231 […]

This is Hausdorff's formula. Recall that $\tau^\lambda$ is the cardinality of the set ${}^\lambda\tau$ of functions $f\!:\lambda\to\tau$, and that $\kappa^+$ is regular for all $\kappa$. Now, there are two possibilities: If $\alpha\ge\tau$, then $2^\alpha\le\tau^\alpha\le(2^\alpha)^\alpha=2^\alpha$, so $\tau^\alpha=2^\alpha$. In particular, if $\alpha\g […]

Fix a model $M$ of a theory for which it makes sense to talk about $\omega$ ($M$ does not need to be a model of set theory, it could even be simply an ordered set with a minimum in which every element has an immediate successor and every element other than the minimum has an immediate predecessor; in this case we could identify $\omega^M$ with $M$ itself). W […]

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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