*Sad news:* Jim Baumgartner passed away. See here.

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Constructible Universe Almost countably chromatic Fast club HOD Weakly compact cardinal Sakurai's Bell inequality free Boolean algebra reflection principles 11P99 Parameterized proxy principle approachability ideal Martin's Axiom Hindman's Theorem Selective Ultrafilter Diamond ccc OCA Knaster 05A17 Foundations Universal Sequences Square-Brackets Partition Relations Chang's conjecture Rock n' Roll Aronszajn tree Forcing Axioms tensor product graph S-Space Kurepa Hypothesis P-Ideal Dichotomy Uniformization Jonsson cardinal incompactness sap Almost-disjoint famiy Singular Density Cohen real PFA Absoluteness Almost Souslin Large Cardinals stationary hitting projective Boolean algebra weak diamond Stevo Todorcevic square Chromatic number Poset Club Guessing weak square 05D10 Mandelbrot set Commutative cancellative semigroups Successor of Regular Cardinal 20M14 Forcing Fat stationary set PFA(S)[S] Minimal Walks Cardinal Invariants b-scale Axiom R middle diamond Small forcing very good scale L-space Coherent tree Successor of Singular Cardinal Ascent Path Slim tree Cardinal function Singular Cofinality Erdos Cardinal Prikry-type forcing Microscopic Approach Singular cardinals combinatorics Singular coﬁnality Ostaszewski square Generalized Clubs Souslin Tree polarized partition relation Erdos-Hajnal graphs Prevalent singular cardinals Reduced Power Rado's conjecture Antichain Whitehead Problem Dushnik-Miller Non-saturation Hedetniemi's conjecture Rainbow sets Hereditarily Lindelöf space Shelah's Strong Hypothesis Partition Relations stationary reflection diamond star

That’s very sad news indeed.

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That is sad.

(*) I will always associate Jim with the phrase “Just Baumgartner it!”. Simon Thomas’s word for bringing in an ultrafilter, seemingly for no reason, and letting it guide your decisions.

(**) I would also like to note that Jim shares his first two names with the actor who portrayed Darth Vader.

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This is very sad news indeed. The email sent around Dartmouth said that he passed away while his whole family was visiting for the holidays, so Jim was fortunate to spend his last moments surrounded by family and high spirits.

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Baumgartner proved that, in contrast to (weak) square,

partialsquare may hold at a singular cardinal (of any cofinality) above a supercomapct carinal. He also proved that after collapsing a weakly comapct cardinal to $\omega_2$, every statinoary subset of $S^2_0$ reflects.These two gems together with an additional argument shows that $\square^*_{\aleph_{\omega_1}}$ may be introduced by a

cofinality-preservingsmall forcing.0 likes