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