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nonmeager set Erdos-Hajnal graphs Ostaszewski square Well-behaved magma Generalized Clubs Strong coloring strongly bounded groups Distributive tree b-scale Constructible Universe full tree Mandelbrot set Reduced Power Singular cardinals combinatorics Sierpinski's onto mapping principle middle diamond coloring number Axiom R unbounded function Forcing Axioms incompactness very good scale HOD Chang's conjecture Weakly compact cardinal xbox Slim tree Strongly Luzin set Ulam matrix indecomposable ultrafilter Amenable C-sequence Aronszajn tree weak diamond Universal Sequences Ineffable cardinal Singular Density Cardinal function tensor product graph Jonsson cardinal Fast club Hindman's Theorem Souslin Tree Filter reflection Dowker space Fat stationary set positive partition relation Lipschitz reduction stationary reflection Ramsey theory over partitions Subtle cardinal Diamond for trees ccc Kurepa Hypothesis Cohen real reflection principles Dushnik-Miller Cardinal Invariants Reflecting stationary set GMA weak Kurepa tree transformations Almost-disjoint family Poset Antichain Successor of Singular Cardinal Subnormal ideal Rainbow sets Nonspecial tree specializable Souslin tree Small forcing Absoluteness Chromatic number projective Boolean algebra Coherent tree Forcing Parameterized proxy principle PFA(S)[S] O-space Uniformly coherent Microscopic Approach Analytic sets stick PFA Diamond Subadditive approachability ideal 54G20 S-Space Hedetniemi's conjecture Iterated forcing Sigma-Prikry Shelah's Strong Hypothesis Square-Brackets Partition Relations Rock n' Roll Commutative cancellative semigroups Generalized descriptive set theory C-sequence OCA Non-saturation Local Club Condensation. Diamond-sharp Erdos Cardinal polarized partition relation Club Guessing Partition Relations Minimal Walks ZFC construction higher Baire space Prevalent singular cardinals Almost Souslin square Large Cardinals Martin's Axiom Successor of Regular Cardinal L-space Fodor-type reflection weak square Singular cofinality Open Access Precaliber super-Souslin tree Vanishing levels Selective Ultrafilter Rado's conjecture Postprocessing function Luzin set countably metacompact free Boolean algebra Uniformly homogeneous Knaster stationary hitting regressive Souslin tree Ascent Path Was Ulam right P-Ideal Dichotomy SNR Greatly Mahlo club_AD Foundations free Souslin tree Subtle tree property Hereditarily Lindelöf space sap diamond star Uniformization AIM forcing Almost countably chromatic Knaster and friends Closed coloring Whitehead Problem square principles Prikry-type forcing Sakurai's Bell inequality
Tag Archives: Diamond
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
Shelah’s solution to Whitehead’s problem
Whitehead problem notes in hebrew : Table of contents Chapter 0 Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 References
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
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
