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,

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 […]

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 […]

Surprisingly, the answer is no due to serious set-theoretic restrictions. If $X$ is an infinite set such that there is a ($\sigma$-additive) measure on $\mathcal P(X)$ that only takes the values 0 and 1, assigns 1 to $X$ and 0 to singletons, then the cardinality $\kappa=|X|$ of $X$ is much much larger than $\mathfrak c=|\mathbb R|$, the cardinality of the se […]

No, you cannot show this. For instance, it is consistent to have infinite Dedekind-finite sets whose power set is still Dedekind-finite. Now, if there is a surjection from $A$ to $\omega$, then there is an injection from $\omega$ (indeed, from $\mathcal P(\omega)$) to $\mathcal P(A)$, so $\mathcal P(A)$ is Dedekind-infinite. Thus, if $\mathcal P(X)$ is infin […]

First, there are some nice examples like $$ e=\sum_{n\ge0}\frac1{n!} $$ or Liouville-like numbers, mentioned in the answers by Wilem2, that can be easily proved to be irrational using the theorem, but for which typically there are simpler irrationality proofs: For $e$, we quickly get that $$0

Note first that if $C$ is uncountable and for each $i\in C$ we have a real number $r_i>0$, then $\sum_i r_i=+\infty$. The point is that for some $n>0$, the family $\{i\in C: r_i>1/n\}$ is uncountable. Of course, in this case there is a countable subfamily whose sum is infinite as well. Now, let $A$ be measurable of infinite measure. If there is an u […]

The theorem says that to prove an implication it is enough to assume the hypothesis and proceed to prove the conclusion. Proofs of that kind tend to be more natural than proofs that conclude the implication directly. Just as in regular mathematical practice: many theorems have the form "Assuming $A$, then we have $B$", and we usually prove them by […]

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!