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

### Archives

### Recent blog posts

- Prikry forcing may add a Souslin tree June 12, 2016
- The reflection principle $R_2$ May 20, 2016
- Prolific Souslin trees March 17, 2016
- Genearlizations of Martin’s Axiom and the well-met condition January 11, 2015
- Many diamonds from just one January 6, 2015
- Happy new jewish year! September 24, 2014
- Square principles April 19, 2014
- Partitioning the club guessing January 22, 2014

### Keywords

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

That’s very sad news indeed.

0 likes

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.

0 likes

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.

0 likes

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