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