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

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

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