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