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