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