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