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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
Generalized Clubs S-Space Singular Cofinality Singular cardinals combinatorics Poset reflection principles Knaster polarized partition relation projective Boolean algebra Prevalent singular cardinals Successor of Regular Cardinal incompactness Foundations diamond star Uniformization Dushnik-Miller weak diamond Large Cardinals weak square P-Ideal Dichotomy Chromatic number Minimal Walks stationary hitting Mandelbrot set Hereditarily Lindelöf space Antichain Club Guessing Diamond stationary reflection free Boolean algebra Axiom R Erdos-Hajnal graphs Cardinal function Erdos Cardinal middle diamond Singular Density Small forcing sap Successor of Singular Cardinal Souslin Tree Square-Brackets Partition Relations approachability ideal Forcing Rainbow sets b-scale Kurepa Hypothesis Shelah's Strong Hypothesis Non-saturation Almost countably chromatic Rado's conjecture square PFA(S)[S] very good scale Cohen real Partition Relations Aronszajn tree Rock n' Roll Prikry-type forcing Sakurai's Bell inequality Whitehead Problem Ostaszewski square
Tag Archives: Generalized Clubs
The failure of diamond on a reflecting stationary set
Joint work with Moti Gitik. Abstract: It is shown that the failure of $\diamondsuit_S$, for a subset $S\subseteq\aleph_{\omega+1}$ that reflects stationarily often, is consistent with GCH and $\text{AP}_{\aleph_\omega}$, relatively to the existence of a supercompact cardinal. This should be comapred with … Continue reading
On guessing generalized clubs at the successors of regulars
Abstract: Konig, Larson and Yoshinobu initiated the study of principles for guessing generalized clubs, and introduced a construction of an higher Souslin tree from the strong guessing principle. Complementary to the author’s work on the validity of diamond and non-saturation … Continue reading
