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,

Let $C$ be the standard Cantor middle-third set. As a consequence of the Baire category theorem, there are numbers $r$ such that $C+r$ consists solely of irrational numbers, see here. What would be an explicit example of a number $r$ with this property? Short of an explicit example, are there any references addressing this question? A natural approach would […]

Suppose $M$ is an inner model (of $\mathsf{ZF}$) with the same reals as $V$, and let $A\subseteq \mathbb R$ be a set of reals in $M$. Suppose further that $A$ is determined in $M$. Under these assumptions, $A$ is also determined in $V$. The point is that since winning strategies are coded by reals, and any possible run of the game for $A$ is coded by a real, […]

Yes. This is obvious if there are no such cardinals. (I assume that the natural numbers of the universe of sets are the true natural numbers. Otherwise, the answer is no, and there is not much else to do.) Assume now that there are such cardinals, and that "large cardinal axiom" is something reasonable (so, provably in $\mathsf{ZFC}$, the relevant […]

Please send an email to mathrev@ams.org, explaining the issue. (This is our all-purpose email address; any mistakes you discover, not just regarding references, you can let us know there.) Give us some time, I promise we'll get to it. However, if it seems as if the request somehow fell through the cracks, you can always contact one of your friendly edit […]

The characterization mentioned by Mohammad in his answer really dates back to Lev Bukovský in the early 70s, and, as Ralf and Fabiana recognize in their note, has nothing to do with $L$ or with reals (in their note, they indicate that after proving their result, they realized they had essentially rediscovered Bukovský's theorem). See MR0332477 (48 #1080 […]

No, not even $\mathsf{DC}$ suffices for this. Here, $\mathsf{DC}$ is the axiom of dependent choice, which is strictly stronger than countable choice. For instance, it is a theorem of $\mathsf{ZF}$ that for any set $X$, the set $\mathcal{WO}(X)$ of subsets of $X$ that are well-orderable has size strictly larger than the size of $X$. This is a result of Tarski […]

I give an example (perhaps the best-known example) below, but let me first discuss equiconsistency rather than straight equivalence. Usually an equiconsistency is really the sort of result you are after anyway: You want to establish that certain statements in the universe where choice holds correspond to determinacy, which implies the failure of choice. The […]

The other answers have correctly identified the issue. Let me highlight the difficulty: it is relatively consistent with the axioms of set theory except for the axiom of choice that there are infinite sets which do not contain a copy of the natural numbers (that is, there are infinite sets $X$ such that there is no injection $f\!:\mathbb N\to X$). This means […]

This is $\aleph_\omega^{\aleph_0}$. First of all, this cardinal is an obvious upper bound. Second, if $A\subseteq\omega$ is infinite, $\prod_{i\in A}\aleph_i$ is clearly at least $\aleph_\omega$. The result follows, by splitting $\omega$ into countably many infinite sets. In general, the rules governing infinite products and exponentials are far from being w […]

If $\lambda$ and $\kappa$ are cardinals, $\lambda^\kappa$ represents the cardinality of the set of functions $f\!:A\to B$ where $A,B$ are fixed sets of cardinality $\kappa,\lambda$ respectively. (One needs to check this is independent of which specific sets $A,B$ we pick, of course.) At least for finite numbers, this is something you may have encountered in […]

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!