Sad news: Jim Baumgartner passed away. See here.
Archives
Recent blog posts
- The S-space problem, and the cardinal invariant $\mathfrak b$ April 4, 2013
- An $S$-space from a Cohen real April 3, 2013
- Forcing with a Souslin tree makes $\mathfrak p=\omega_1$ April 1, 2013
- The S-space problem, and the cardinal invariant $\mathfrak p$ March 28, 2013
- Jones’ theorem on the cardinal invariant $\mathfrak p$ March 26, 2013
- Erdős 100 March 26, 2013
- Bell’s theorem on the cardinal invariant $\mathfrak p$ March 21, 2013
- The $\Delta$-system lemma: an elementary proof March 20, 2013
Keywords
Prikry-type forcing weak diamond Cohen real Rock n' Roll Successor of Regular Cardinal Aronszajn tree free Boolean algebra Singular Density Rainbow sets Rado's conjecture approachability ideal Diamond Antichain middle diamond Foundations stationary hitting Square-Brackets Partition Relations Knaster polarized partition relation Shelah's Strong Hypothesis Uniformization PFA(S)[S] Partition Relations Kurepa Hypothesis Singular cardinals combinatorics S-Space Prevalent singular cardinals diamond star Poset Club Guessing Mandelbrot set Large Cardinals Sakurai's Bell inequality P-Ideal Dichotomy Chromatic number Minimal Walks Cardinal function Generalized Clubs weak square square projective Boolean algebra Axiom R Small forcing Whitehead Problem Erdos-Hajnal graphs b-scale Hereditarily Lindelöf space Singular Cofinality stationary reflection Successor of Singular Cardinal Almost countably chromatic Souslin Tree Dushnik-Miller Ostaszewski square incompactness Non-saturation very good scale Erdos Cardinal sap reflection principles Forcing
That’s very sad news indeed.
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.
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.
Baumgartner proved that, in contrast to (weak) square, partial square 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-preserving small forcing.