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very good scale Forcing Axioms Square-Brackets Partition Relations free Souslin tree Iterated forcing Precaliber Poset free Boolean algebra Almost-disjoint family super-Souslin tree SNR Fodor-type reflection Non-saturation polarized partition relation tensor product graph Well-behaved magma Sigma-Prikry Closed coloring Parameterized proxy principle ccc Lipschitz reduction Ineffable cardinal Hindman's Theorem middle diamond Intersection model Partition Relations Knaster and friends specializable Souslin tree Cohen real Absoluteness coloring number Amenable C-sequence GMA HOD Successor of Regular Cardinal b-scale Ulam matrix Foundations higher Baire space Commutative projection system Fast club xbox projective Boolean algebra Singular cardinals combinatorics Singular cofinality Strong coloring Forcing Postprocessing function Shelah's Strong Hypothesis Cardinal function Mandelbrot set Commutative cancellative semigroups Ascent Path Ramsey theory over partitions Uniformly homogeneous Prikry-type forcing Filter reflection Subtle cardinal Diamond C-sequence Strongly compact cardinal Ostaszewski square Sakurai's Bell inequality countably metacompact Chang's conjecture OCA Rado's conjecture Uniformly coherent Prevalent singular cardinals Nonspecial tree Erdos Cardinal Knaster S-Space indecomposable ultrafilter Almost countably chromatic reflection principles Antichain Diamond for trees Minimal Walks square principles ZFC construction club_AD diamond star Dushnik-Miller PFA Large Cardinals Universal Sequences Constructible Universe Small forcing stationary reflection Uniformization unbounded function positive partition relation PFA(S)[S] Cardinal Invariants Club Guessing weak square Aronszajn tree weak diamond full tree incompactness Local Club Condensation. Slim tree Vanishing levels Luzin set Successor of Singular Cardinal Fat stationary set Countryman line Generalized descriptive set theory strongly bounded groups Subtle tree property Almost Souslin Weakly compact cardinal Distributive tree Erdos-Hajnal graphs Coherent tree Hereditarily Lindelöf space Open Access Dowker space Greatly Mahlo Was Ulam right? O-space Martin's Axiom Diamond-sharp Microscopic Approach Souslin Tree regressive Souslin tree Jonsson cardinal Rock n' Roll Chromatic number Whitehead Problem approachability ideal Singular Density square Generalized Clubs Strongly Luzin set Reflecting stationary set 54G20 transformations Rainbow sets Subnormal ideal AIM forcing Analytic sets stick P-Ideal Dichotomy Selective Ultrafilter Hedetniemi's conjecture Reduced Power Sierpinski's onto mapping principle Respecting tree Kurepa Hypothesis nonmeager set stationary hitting weak Kurepa tree sap L-space Subadditive Axiom R
Tag Archives: Diamond
The search for diamonds
Abstract: This is a review I wrote for the Bulletin of Symbolic Logic on the following papers: Saharon Shelah, Middle Diamond, Archive for Mathematical Logic, vol. 44 (2005), pp. 527–560. Saharon Shelah, Diamonds, Proceedings of the American Mathematical Society, vol. … Continue reading
Posted in Publications, Reviews, Squares and Diamonds
Tagged Diamond, middle diamond, weak diamond, weak square
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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
A relative of the approachability ideal, diamond and non-saturation
Abstract: Let
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
