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