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Parameterized proxy principle Amenable C-sequence Foundations Successor of Regular Cardinal Ulam matrix reflection principles full tree Kurepa Hypothesis C-sequence super-Souslin tree stick Iterated forcing Ascending path Interval topology on trees weak diamond Small forcing ZFC construction Poset Constructible Universe Luzin set specializable Souslin tree Square-Brackets Partition Relations Diamond for trees P-Ideal Dichotomy Dowker space Strong coloring Successor of Singular Cardinal Forcing Shelah's Strong Hypothesis Sigma-Prikry Prevalent singular cardinals Cardinal Invariants Ascent Path S-Space Reflecting stationary set ccc Analytic sets L-space incompactness square PFA(S)[S] Chang's conjecture Ramsey theory over partitions regressive Souslin tree Fodor-type reflection Martin's Axiom Sakurai's Bell inequality Souslin Tree Rock n' Roll Cardinal function Commutative projection system transformations Non-saturation PFA Lipschitz reduction unbounded function Knaster and friends Universal Sequences Ostaszewski square Postprocessing function square principles Erdos-Hajnal graphs Precaliber Uniformly homogeneous Commutative cancellative semigroups Prikry-type forcing approachability ideal Subnormal ideal Fat stationary set Nonspecial tree Open Access weak square Microscopic Approach higher Baire space Uniformization Absoluteness Jonsson cardinal Chromatic number Diamond Uniformly coherent Weakly compact cardinal Distributive tree Generalized descriptive set theory Respecting tree Diamond-sharp 54G20 Countryman line free Souslin tree Strongly Luzin set Hindman's Theorem Vanishing levels stationary hitting diamond star HOD Local Club Condensation. SNR Singular cardinals combinatorics Singular Density Hereditarily Lindelöf space Singular cofinality nonmeager set Almost Souslin Was Ulam right? club_AD Rado's conjecture strongly bounded groups Reduced Power Minimal Walks Rainbow sets weak Kurepa tree tensor product graph Selective Ultrafilter Generalized Clubs Strongly compact cardinal xbox Large Cardinals Well-behaved magma free Boolean algebra coloring number Whitehead Problem Antichain Closed coloring positive partition relation Greatly Mahlo middle diamond projective Boolean algebra indecomposable filter Knaster OCA Club Guessing Dushnik-Miller perfectly normal Intersection model Axiom R Forcing with side conditions Erdos Cardinal Monotonically far countably metacompact Cohen real O-space Aronszajn tree Subtle tree property Entangled linear order Filter reflection Sierpinski's onto mapping principle Coherent tree GMA Mandelbrot set Forcing Axioms stationary reflection Partition Relations AIM forcing Subadditive Almost-disjoint family Ineffable cardinal Hedetniemi's conjecture Partition relations for trees Subtle cardinal Slim tree Almost countably chromatic b-scale polarized partition relation Fast club sap very good scale
Tag Archives: diamond star
Square with built-in diamond-plus
Joint work with Ralf Schindler. Abstract. We formulate combinatorial principles that combine the square principle with various strong forms of diamond, and prove that the strongest amongst them holds in $L$ for every infinite cardinal. As an application, we prove that … Continue reading
Posted in Publications, Squares and Diamonds
Tagged 03E05, 03E45, Almost Souslin, diamond star, Kurepa Hypothesis, Minimal Walks, Respecting tree, square, xbox
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A Kurepa tree from diamond-plus
Recall that $T$ is said to be a $\kappa$-Kurepa tree if $T$ is a tree of height $\kappa$, whose levels $T_\alpha$ has size $\le|\alpha|$ for co-boundedly many $\alpha<\kappa$, and such that the set of branches of $T$ has size $>\kappa$. … Continue reading
Posted in Blog, Expository
Tagged diamond star, Kurepa Hypothesis
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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
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
