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