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,

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 […]

The only reference I know for precisely these matters is the handbook chapter MR2768702. Koellner, Peter; Woodin, W. Hugh. Large cardinals from determinacy. In Handbook of set theory. Vols. 1, 2, 3, 1951–2119, Springer, Dordrecht, 2010. (Particularly, section 7.) For closely related topics, see also the work of Yong Cheng (and of Cheng and Schindler) on Harr […]

As other answers point out, yes, one needs choice. The popular/natural examples of models of ZF+DC where all sets of reals are measurable are models of determinacy, and Solovay's model. They are related in deep ways, actually, through large cardinals. (Under enough large cardinals, $L({\mathbb R})$ of $V$ is a model of determinacy and (something stronge […]

Throughout the question, we only consider primes of the form $3k+1$. A reference for cubic reciprocity is Ireland & Rosen's A Classical Introduction to Modern Number Theory. How can I count the relative density of those $p$ (of the form $3k+1$) such that the equation $2=3x^3$ has no solutions modulo $p$? Really, even pointers on how to say anything […]

Using the regularity of $\kappa$ and the fact that the infinite cardinal $\lambda$ is less than $\kappa$, Jech notes that $$ \kappa^\lambda=\bigcup_{\alpha

A set $x$ is hereditarily $\varphi$ if and only if every member of its transitive closure (including $x$ itself) has property $\varphi$. For instance, being hereditarily finite means not just that $x$ is finite, but also every member of $x$ is finite, and every member of every member of $x$, and so on. (Note that in the absence of foundation, this is a bit p […]

Let $s$ be the supremum of the $\mu$-measures of members of $\mathcal G$. By definition of supremum, for each $n$, there is $G_n\in\mathcal G$ with $\mu(G_n)>s-1/n$. Letting $G=\bigcup_n G_n$, then $G\in \mathcal G$ since $\mathcal G$ is closed under countable unions, and $\mu(G)=s$, since it is at least $\sup_n\mu(G_n)$ but it is at most $s$ (by definiti […]

The result you are trying to prove is false. For example, if $a=\omega+1$ and $b=\omega+\omega$, then $a+b=\omega\cdot 3>b$. Here is what is true: first, the key result you should establish (by induction) is that An ordinal $\alpha>0$ has the property that for all $\beta

Very briefly: Yes, there are several programs being developed that can be understood as pursuing new axioms for set theory. For the question itself of whether pursuing new axioms is a reasonably line of inquiry, see the following (in particular, the paper by John Steel): MR1814122 (2002a:03007). Feferman, Solomon; Friedman, Harvey M.; Maddy, Penelope; Steel, […]

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!