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