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