(If someone has a version in higher resolution, or pictures of the conference, please contact John Steel, or myself.)

A very incomplete key, possibly with mistakes:

First row: ?, Diego Rojas-Rebolledo, ?, Leo Harrington, Ernest Schimmerling.

Second: Peter Koekpe; Alexandra, Hugh, and Christine Woodin; Xianghui Shi, me, John Clemens.

Third: John Steel, Alessandro Andretta, Tony Martin.

Fourth: Stevo Todorcevic, Paul Corazza, Philip Welch, Ilijah Farah, Qi Feng, ?, Martin Zeman, Robert Solovay, Richard Laver, Erik Closson (?), James Cummings.

Fifth: ?, Itay Neeman, Thomas Jech, Greg Hjorth, Joan Moschovakis (?), Yiannis Moschovakis, Matthew Foreman (?), Ted Slaman, Jindra Zapletal, Joan Bagaria.

Sixth: Benedikt Löwe, ?, Jean Larson, Bill Mitchell, ?, Carlos di Prisco, ?, Mike Oliver, ?, Lorenz Halbeisen, Derrick Duboise, Peter Koellner.

Seventh, etc: Herb Enderton, ?, ?, Joel Hamkins, Alain Louveau, Slawomir Solecki, ?, Mack Stanley, ?, ?, Tomek Bartoszynski, Paul Larson, Lisa Marks, Richard Ketchersid. ?

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[…] this picture a few days ago, when looking at the old photos from the Martin Conference. I posted here the group picture from that conference. John Steel should be posting the other pictures soon (well, […]

Georgii: Let me start with some brief remarks. In a series of three papers: a. Wacław Sierpiński, "Contribution à la théorie des séries divergentes", Comp. Rend. Soc. Sci. Varsovie 3 (1910) 89–93 (in Polish). b. Wacław Sierpiński, "Remarque sur la théorème de Riemann relatif aux séries semi-convergentes", Prac. Mat. Fiz. XXI (1910) 17–20 […]

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This is Theorem 39 in the paper (see Theorem 4.(i) for a user-friendly preview). But the fact that $(2^\kappa)^+\to(\kappa^+)^2_\kappa$ is older (1946) and due to Erdős, see here: Paul Erdős. Some set-theoretical properties of graphs, Univ. Nac. Tucumán. Revista A. 3 (1942), 363-367 MR5,151d. (Anyway, it is probably easier to read a more modern presentation, […]

This is a nice problem. Here is what I know. (Below, I refer to the Handbook. This is the Handbook of Set Theory, Foreman, Kanamori, eds., Springer, 2010.) First of all, the consistency of the failure of diamond at a weakly compact cardinal seems open. Woodin has asked this explicitly, I do not know if the question itself is due to him. Of course, $\diamonds […]

I thought about this question a while ago, while teaching a topics course. Since one can easily check that $${}|{\mathbb R}|=|{\mathcal P}({\mathbb N})|$$ by a direct construction that does not involve diagonalization, the question can be restated as: Is there a proof of Cantor's theorem that ${}|X|

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Yes. In fact, by a counting argument, most dense co-dense sets are neither $G_\delta$ nor $F_\sigma$. The point is that there are exactly as many $G_\delta$ or $F_\sigma$ as there are real numbers, but there are as many dense co-dense sets as there are sets of real numbers. In somewhat more detail: There are only countably many rationals, so there are counta […]

There are quite a few examples in analysis, typically through the use of transfinite induction or transfinite recursion of length $\omega_1$. The Baire-Cantor stationary principle states that if $C_0\supseteq C_1\supseteq C_2\supseteq\dots\supseteq C_\alpha\supseteq\dots$, $\alpha

I’ll try to post a key over the next few days. [

Edit:Added, though terribly incomplete.][…] this picture a few days ago, when looking at the old photos from the Martin Conference. I posted here the group picture from that conference. John Steel should be posting the other pictures soon (well, […]