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Dushnik-Miller Local Club Condensation. Partition Relations Fat stationary set Diamond for trees Rado's conjecture full tree Sigma-Prikry Analytic sets Well-behaved magma PFA Strongly compact cardinal Knaster 54G20 Open Access Ineffable cardinal Reflecting stationary set free Souslin tree Singular cofinality Fast club Commutative cancellative semigroups sap Postprocessing function Square-Brackets Partition Relations Singular Density Countryman line Chromatic number Aronszajn tree Distributive tree Chang's conjecture Prevalent singular cardinals Axiom R weak square tensor product graph Club Guessing Forcing Axioms Diamond-sharp Vanishing levels Commutative projection system P-Ideal Dichotomy stick Knaster and friends Was Ulam right? projective Boolean algebra diamond star positive partition relation super-Souslin tree Entangled linear order Hedetniemi's conjecture OCA PFA(S)[S] perfectly normal Filter reflection AIM forcing Cardinal Invariants Subnormal ideal Mandelbrot set Strongly Luzin set stationary reflection coloring number Precaliber Ascending path Universal Sequences Forcing with side conditions Sakurai's Bell inequality ccc Ramsey theory over partitions Successor of Regular Cardinal Amenable C-sequence indecomposable filter Erdos-Hajnal graphs Jonsson cardinal Subadditive Intersection model Weakly compact cardinal strongly bounded groups stationary hitting Constructible Universe Lipschitz reduction L-space transformations Luzin set Reduced Power Uniformly coherent ZFC construction Small forcing higher Baire space xbox square principles O-space Partition relations for trees Subtle tree property Subtle cardinal polarized partition relation weak Kurepa tree specializable Souslin tree Almost countably chromatic Fodor-type reflection approachability ideal square Closed coloring Erdos Cardinal very good scale Selective Ultrafilter Greatly Mahlo club_AD incompactness Large Cardinals Ascent Path Coherent tree Strong coloring weak diamond countably metacompact Whitehead Problem Absoluteness Minimal Walks Non-saturation Antichain nonmeager set Poset Diamond free Boolean algebra Parameterized proxy principle regressive Souslin tree Hereditarily Lindelöf space Almost-disjoint family Sierpinski's onto mapping principle Cohen real Hindman's Theorem Successor of Singular Cardinal SNR Almost Souslin Iterated forcing Souslin Tree C-sequence Microscopic Approach Shelah's Strong Hypothesis Monotonically far S-Space Uniformization Rock n' Roll Respecting tree Rainbow sets Martin's Axiom Uniformly homogeneous Kurepa Hypothesis HOD unbounded function GMA Ostaszewski square middle diamond Ulam matrix Foundations Slim tree Generalized descriptive set theory Generalized Clubs Interval topology on trees Nonspecial tree Cardinal function Prikry-type forcing b-scale Singular cardinals combinatorics Forcing Dowker space reflection principles
Tag Archives: Fat stationary set
Distributive Aronszajn trees
Joint work with Ari Meir Brodsky. Abstract. Ben-David and Shelah proved that if $\lambda$ is a singular strong-limit cardinal and $2^\lambda=\lambda^+$, then $\square^*_\lambda$ entails the existence of a $\lambda$-distributive $\lambda^+$-Aronszajn tree. Here, it is proved that the same conclusion remains … Continue reading
Chain conditions of products, and weakly compact cardinals
Abstract. The history of productivity of the $\kappa$-chain condition in partial orders, topological spaces, or Boolean algebras is surveyed, and its connection to the set-theoretic notion of a weakly compact cardinal is highlighted. Then, it is proved that for every … Continue reading
Posted in Partition Relations, Publications
Tagged Aronszajn tree, ccc, Fat stationary set, Minimal Walks, square, Weakly compact cardinal
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The Ostaszewski square, and homogeneous Souslin trees
Abstract: Assume GCH and let $\lambda$ denote an uncountable cardinal. We prove that if $\square_\lambda$ holds, then this may be witnessed by a coherent sequence $\left\langle C_\alpha \mid \alpha<\lambda^+\right\rangle$ with the following remarkable guessing property: For every sequence $\langle A_i\mid i<\lambda\rangle$ … Continue reading
Posted in Publications, Souslin Hypothesis, Squares and Diamonds
Tagged 03E05, 03E35, Club Guessing, Fat stationary set, Ostaszewski square, Souslin Tree
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