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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
Prikry-type forcing stationary hitting Diamond very good scale Knaster Aronszajn tree Whitehead Problem stationary reflection Rado's conjecture S-Space Rock n' Roll Chromatic number middle diamond Singular Cofinality Hereditarily Lindelöf space reflection principles Poset Sakurai's Bell inequality sap Large Cardinals Singular cardinals combinatorics Minimal Walks Cohen real weak square Dushnik-Miller Foundations diamond star weak diamond Club Guessing Small forcing b-scale Souslin Tree P-Ideal Dichotomy Successor of Singular Cardinal Uniformization free Boolean algebra Successor of Regular Cardinal Antichain incompactness Mandelbrot set Rainbow sets projective Boolean algebra Almost countably chromatic Axiom R PFA(S)[S] Square-Brackets Partition Relations Erdos Cardinal Erdos-Hajnal graphs approachability ideal Shelah's Strong Hypothesis Kurepa Hypothesis Singular Density Cardinal function polarized partition relation square Generalized Clubs Forcing Partition Relations Ostaszewski square Non-saturation Prevalent singular cardinals
Tag Archives: diamond star
Jensen’s diamond principle and its relatives
This is chapter 6 in the book Set Theory and Its Applications (ISBN: 0821848127). Abstract: We survey some recent results on the validity of Jensen’s diamond principle at successor cardinals. We also discuss weakening of this principle such as club … Continue reading
A relative of the approachability ideal, diamond and non-saturation
Abstract: Let $\lambda$ denote a singular cardinal. Zeman, improving a previous result of Shelah, proved that $\square^*_\lambda$ together with $2^\lambda=\lambda^+$ implies $\diamondsuit_S$ for every $S\subseteq\lambda^+$ that reflects stationarily often. In this paper, for a subset $S\subset\lambda^+$, a normal subideal of … Continue reading
