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

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

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