I was recently sent this picture, from the October 1989 set theory workshop at the MSRI as part of its Logic Year.

Paul Larson suggested to crowdsource the problem of identifying the attendants in the picture. Please feel free to participate in the comments and let’s see how far we get.

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To get things started, a very small sample: In the front row, we have Saharon, Menachem and Marion Scheepers. In the next row, I see Jean Larson, Carlos Montenegro and Ted Slaman. In the next row, Joan Moschovakis, Aki, Robert Soare, Adrian, Philip Welch, Hugh, Jech, Howard Becker, Carlos Di Prisco. In the next, John Addison, Solovay, Alekos, Andreas Blass, Joan Bagaria. Somewhere in there, you also find Paul Corazza, Ernest, Bill Mitchell, Tomek, Matt Foreman, John Steel, Tony, Yiannis, James Cummings, Carol Wood, Richard Shore, Cherlin.

What a great picture, thanks for posting it! It is Bill Weiss in the first row, sitting first on the left. Isn’t it Jörg Brendle in the front row, 4 left from Saharon?

Kai Hauser is next to James Cummings. James Baumgartner is NNW of Jean Larson. MacLane, Jockusch, Harrington, Soare, Mathias and Welch are all in a row? Solovay and Halmos behind them? Steve Jackson near Blass? Louveau in front of Joan?

Back row, from left: Achim Ditzen, ?, James Cummings, Kai Hauser…

Second row: Aki Kanamori, ?, ?, Carl Jockusch, Leo Harrington, Bob Soare, Adrian Mathias, Philip Welch, ?, Hugh Woodin, Alain Louveau, Thomas Jech, …

Front row, starting with: Jean Larson, Wolfram Pohlers, Stefan Bilaniuk, …, Joerg Brendle (with crossed legs in front) ….Ted Slaman….Menachem Magidor

At left, third row: Charles Steinhorn, Yiannis Moschovakis (with John Steel behind), …….., James Baumgartner, Haim Judah, John Addison, Robert Solovay, Paul Halmos, Alexander Kechris, Andreas Blass, Joan Bagaria, ?, Carol Wood, ……, Bill Mitchell

behind them: Matthew Foreman, ….., Tomek Bartoczynski, Greg Cherlin,

I know many more, and can post later, if you can indicate which people you don’t yet know.

Perhaps the following may clarify the comments: for any ordinal $\delta$, there is a Boolean-valued extension of the universe of sets where $2^{\aleph_0}>\aleph_\delta$ holds. If you rather talk of models than Boolean-valued extensions, what this says is that we can force while preserving all ordinals, and in fact all initial ordinals, and make the contin […]

I do not know of any active set theorists who think large cardinals are inconsistent. At least, within the realm of cardinals we have seriously studied. [Reinhardt suggested an ultimate axiom of the form "there is a non-trivial elementary embedding $j:V\to V$". Though some serious set theorists found it of possible interest immediately following it […]

There is a fantastic (and not too well-known) result of Shelah stating that $L({\mathcal P}(\lambda))$ is a model of choice whenever $\lambda$ is a singular strong limit of uncountable cofinality. This is a consequence of a more general theorem that can be found in 4.6/6.7 of "Set Theory without choice: not everything on cofinality is possible", Ar […]

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 […]

Yes, it is consistent to have such cardinals. In fact, it is consistent relative to an inaccessible cardinal that $\omega\to(\omega)^\omega_2$. This is a famous result of Mathias, in MR0491197 (58 #10462). Mathias, A. R. D. Happy families. Ann. Math. Logic 12 (1977), no. 1, 59–111. (It is still open whether the inaccessible cardinal is required.) The result […]

The inductive definition of forcing (by complexity of formulas) gives in particular that $p$ forces $\lnot\psi$ if and only if no extension of $p$ forces $\psi$. That is exactly what is being claimed. As for why this general fact about forcing of negations holds, it is either immediate from the fact that a statement holds in a generic extension if and only i […]

The principle $\lozenge$ (diamond) is in a sense the right set-theoretic version of the continuum hypothesis, as it presents it instead as a reflection principle. Formally, it asserts that there is a diamond sequence, that is, a sequence $(A_\alpha:\alpha

Unfortunately, Maddy is being imprecise in her use of terminology and the surrounding explanation. The mention of Borel in page 496 is a good hint that the notion she is discussing is that of being strong measure zero, as suggested in the comments. A set of reals is (or has) measure zero if and only if for any $\epsilon>0$ it can be covered by countably m […]

Note that $\alpha\mapsto\|c_\alpha^\lambda\|_S$ is strictly increasing (trivially): After all, $$\{\delta\in S\mid c_\beta^\lambda(\delta)\ge c_\alpha^\lambda(\delta)\}=\{\delta\in S\mid\beta\ge \alpha\}=\emptyset$$ if $\beta

To get things started, a very small sample: In the front row, we have Saharon, Menachem and Marion Scheepers. In the next row, I see Jean Larson, Carlos Montenegro and Ted Slaman. In the next row, Joan Moschovakis, Aki, Robert Soare, Adrian, Philip Welch, Hugh, Jech, Howard Becker, Carlos Di Prisco. In the next, John Addison, Solovay, Alekos, Andreas Blass, Joan Bagaria. Somewhere in there, you also find Paul Corazza, Ernest, Bill Mitchell, Tomek, Matt Foreman, John Steel, Tony, Yiannis, James Cummings, Carol Wood, Richard Shore, Cherlin.

I’m fairly confident that third from the left in the front row is Alan Dow.

What a great picture, thanks for posting it! It is Bill Weiss in the first row, sitting first on the left. Isn’t it Jörg Brendle in the front row, 4 left from Saharon?

Kai Hauser is next to James Cummings. James Baumgartner is NNW of Jean Larson. MacLane, Jockusch, Harrington, Soare, Mathias and Welch are all in a row? Solovay and Halmos behind them? Steve Jackson near Blass? Louveau in front of Joan?

Here is a start.

Back row, from left: Achim Ditzen, ?, James Cummings, Kai Hauser…

Second row: Aki Kanamori, ?, ?, Carl Jockusch, Leo Harrington, Bob Soare, Adrian Mathias, Philip Welch, ?, Hugh Woodin, Alain Louveau, Thomas Jech, …

Front row, starting with: Jean Larson, Wolfram Pohlers, Stefan Bilaniuk, …, Joerg Brendle (with crossed legs in front) ….Ted Slaman….Menachem Magidor

At left, third row: Charles Steinhorn, Yiannis Moschovakis (with John Steel behind), …….., James Baumgartner, Haim Judah, John Addison, Robert Solovay, Paul Halmos, Alexander Kechris, Andreas Blass, Joan Bagaria, ?, Carol Wood, ……, Bill Mitchell

behind them: Matthew Foreman, ….., Tomek Bartoczynski, Greg Cherlin,

I know many more, and can post later, if you can indicate which people you don’t yet know.