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

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### Keywords

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

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