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