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

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

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