Help us identify all mathematicians in this picture (click on it for a larger version). Please post comments here, on G+, or email me or Paul Larson.

The picture will appear in the book of proceedings of the Woodin conference, http://logic.harvard.edu/woodin_meeting.html. (Thanks to David Schrittesser for allowing us to use it.)

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Douglas Blue
Scott Cramer
Liuzhen Wu
Nam Trang
Daisuke Ikegami
Xianghui Shi
Vincenzo Dimonte
Joseph Van Name
Tony Martin
Alexander Kechris
Joan Bagaria
Laura Fontanella
Paul McKenney
Kaethe Minden
Kameryn Williams
Paul Larson
Sheila Miller
Ronald Jensen
Steve Homer
Juliette Kennedy
David Schrittesser
W Hugh Woodin
Gunter Fuchs
Arthur Apter
Menachem Magidor
Charles Parsons
Jouko Väänänen
Ralf Schindler
Rehana Patel
Nate Ackerman
John Steel
George Kafkoulis
Ilijas Farah
Martin Zeman
Assaf Peretz
Grigor Sargsyan
Akihiro Kanamori
Trevor Wilson
Maryanthe Malliaris
Hossein Lamei Ramandi
Philip Welch
H Garth Dales
Derrick DuBose
Gabriel Goldberg
Joel David Hamkins
Ted Slaman
Jacob Davis
Doug Hoffman
Joshua Reagan
Matthew Foreman
Zeynep Soysal
Daniel Rodríguez
Peter Koellner

(On behalf of all the editors of the volume, thanks to Benedikt Löwe, Iian Smythe, Miha Habič, Joel David Hamkins, Asaf Karagila, Yizheng Zhu, and Derrick DuBose.)

Here are a few more:
– Nate Ackerman’s face is visible next to Ralf Schindler.
– Maryanthe Malliaris is between Grigor and me.
– Kaethe Minden is in front between Martin and Woodin.
– Jacob Davis is in front in red coat.
– Joseph van Name is in red shirt in front of Joan Bagaria.

Matt Foreman to the right of Derrick DuBose, Hossein Lamei Ramandi (I think) to the left behind Philip Welch, George Kafkoulis (I think) behind Ilijas Farah, Paul McKenney in green windbreaker at back behind Laure Fontanella,

In set theory, definitely the notion of a Woodin cardinal. First, it is not an entirely straightforward notion to guess. Significant large cardinals were up to that point defined as critical points of certain elementary embeddings. This is not the case here: Woodin cardinals need not be measurable. If $\kappa$ is Woodin, then $V_\kappa$ is a model of set the […]

The first example that came to mind was MR0270881 (42 #5764) van der Waerden, B. L. How the proof of Baudet's conjecture was found. 1971 Studies in Pure Mathematics (Presented to Richard Rado) pp. 251–260 Academic Press, London. There, van der Waerden describes some of the history as well as his proof of his well-known theorem. Another example: MR224589 […]

The key reference for this is MR0799042 (87d:03141). Henle, J. M.; Mathias, A. R. D.; Woodin, W. Hugh. A barren extension. In Methods in mathematical logic (Caracas, 1983), C. A. Di Prisco, editor, 195–207, Lecture Notes in Math., 1130, Springer, Berlin, 1985. There, Henle, Mathias, and Woodin start with $L(\mathbb R)$ under the assumption of determinacy (an […]

This is consistent, at least under a rather tame large cardinal assumption. (One can also produce examples by manipulating Dedekind finite sets, but Asaf's answer addresses this. The answer here works even in the context of $\mathsf{DC}$.) For instance, see MR3612001. Conley, Clinton T.; Miller, Benjamin D. Measure reducibility of countable Borel equiva […]

You should really stop writing soups of symbols and just describe in words what you are doing. It saves a coding headache on your side and a decoding headache on the reader's. Anyway, the formula seems to say that if for every ordinal there is a larger cardinal with property $\psi$, then there is a bijection between the class of ordinals and that of car […]

Your idea is sound, but it requires more work. As pointed out, you have only described so far a very small subcollection of the Borel sets. Instead, show that you can associate to each Borel set a code that keeps track of the "history" of its construction starting from basic open sets, and then count the number of such codes. There is a lot of leew […]

Yes, the minimal such model is $L[0^\sharp]$. This model can be built by stages, just as $L$, starting with the empty set, taking unions at limit stages, and at each successor stage $\alpha+1$ taking the collection of subsets of $L_\alpha[0^\sharp]$ definable in $(L_\alpha[0^\sharp],\in,0^\sharp)$ from parameters. Here, $0^\sharp$ can be thought of as a set […]

There are several issues here. An obvious one is that there are only so many proofs and many more ordinals, so there are ordinals that we cannot even refer to within the theory, so of course the theory cannot prove anything about them. This is somewhat subtle, as there are models of set theory that are pointwise definable, so that any $x$ in the model is def […]

Check first that $\liminf |a_n|=0$ if and only if some subsequence of the $a_n$ converges to $0$. Assuming that $\liminf|a_n|=0$, use the equivalence above to show that, indeed, there is a subsequence $(a_{n_k})_{k\ge0}$ that, not only converges to 0, but does it very quickly, say $|a_{n_k}|

There are 53 people in the picture.

Roughly from left to right,

Douglas Blue

Scott Cramer

Liuzhen Wu

Nam Trang

Daisuke Ikegami

Xianghui Shi

Vincenzo Dimonte

Joseph Van Name

Tony Martin

Alexander Kechris

Joan Bagaria

Laura Fontanella

Paul McKenney

Kaethe Minden

Kameryn Williams

Paul Larson

Sheila Miller

Ronald Jensen

Steve Homer

Juliette Kennedy

David Schrittesser

W Hugh Woodin

Gunter Fuchs

Arthur Apter

Menachem Magidor

Charles Parsons

Jouko Väänänen

Ralf Schindler

Rehana Patel

Nate Ackerman

John Steel

George Kafkoulis

Ilijas Farah

Martin Zeman

Assaf Peretz

Grigor Sargsyan

Akihiro Kanamori

Trevor Wilson

Maryanthe Malliaris

Hossein Lamei Ramandi

Philip Welch

H Garth Dales

Derrick DuBose

Gabriel Goldberg

Joel David Hamkins

Ted Slaman

Jacob Davis

Doug Hoffman

Joshua Reagan

Matthew Foreman

Zeynep Soysal

Daniel Rodríguez

Peter Koellner

(On behalf of all the editors of the volume, thanks to Benedikt Löwe, Iian Smythe, Miha Habič, Joel David Hamkins, Asaf Karagila, Yizheng Zhu, and Derrick DuBose.)

Some more:

– Douglas Blue (top left corner)

– Hossein Ramandi (back row, between Trevor Wilson and Phillip Welch)

– Matt Foreman (far right)

Thank you, Miha!

Here are a few more:

– Nate Ackerman’s face is visible next to Ralf Schindler.

– Maryanthe Malliaris is between Grigor and me.

– Kaethe Minden is in front between Martin and Woodin.

– Jacob Davis is in front in red coat.

– Joseph van Name is in red shirt in front of Joan Bagaria.

Behind Nate might be (partial forehead view only) Rehana Patel?

Matt Foreman to the right of Derrick DuBose, Hossein Lamei Ramandi (I think) to the left behind Philip Welch, George Kafkoulis (I think) behind Ilijas Farah, Paul McKenney in green windbreaker at back behind Laure Fontanella,

Thank you, James.

Sorry, it seems it should be Joseph Van Name, with a capital V. (And also I usually go by my full name.)

Thanks, Joel! We are almost done; I think that, barring mistakes and typos, there are only 4 spots pending.

Can you point out the locations of the missing names?

Joel, I added descriptions at the beginning of the list.

The man behind Nam and in front of Daisuke is Liuzhen Wu. Xianghui Shi is misspelled.

Thank you, Yizheng.

Are we sure the last two are not set theorists from the future, that traveled back in time to attend this meeting?

Success!