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

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### Recent blog posts

- Partitioning the club guessing January 22, 2014
- Walk on countable ordinals: the characteristics December 1, 2013
- Polychromatic colorings November 26, 2013
- Universal binary sequences November 14, 2013
- Syndetic colorings with applications to S and L October 26, 2013
- Open coloring and the cardinal invariant $\mathfrak b$ October 8, 2013
- Gabriel Belachsan (14/5/1976 – 20/8/2013) August 20, 2013
- PFA and the tree property at $\aleph_2$ June 9, 2013

### Keywords

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

- Luzin sets and generalizations
- Nonuniversal colorings in ZFC
- Large Sets
- Infinite-dimensional Jonsson algebras
- Strong colorings without nontrivial polychromatic sets
- Infinite-dimensional polychromatic colorings
- Polychromatic colorings of the first uncountable cardinal
- From colorings to topology
- From topology to colorings
- Anti-Ramsey colorings of the rational numbers, part 2

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