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