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Ascending path sap Rado's conjecture O-space Postprocessing function Intersection model Uniformly homogeneous square xbox countably metacompact P-Ideal Dichotomy Ostaszewski square Open Access Successor of Regular Cardinal Square-Brackets Partition Relations Subtle cardinal Hedetniemi's conjecture Singular cardinals combinatorics Uniformization Cohen real Rainbow sets Club Guessing b-scale Forcing with side conditions Strong coloring approachability ideal Sierpinski's onto mapping principle Slim tree Analytic sets Whitehead Problem unbounded function free Souslin tree Precaliber super-Souslin tree Large Cardinals Fodor-type reflection Jonsson cardinal Forcing Generalized descriptive set theory Non-saturation Souslin Tree Filter reflection Erdos-Hajnal graphs Partition Relations Parameterized proxy principle Hindman's Theorem Fat stationary set Respecting tree Cardinal function square principles Singular cofinality coloring number Mandelbrot set PFA(S)[S] Interval topology on trees Microscopic Approach Almost Souslin Greatly Mahlo Minimal Walks Commutative projection system Coherent tree higher Baire space OCA Countryman line Reduced Power stick Shelah's Strong Hypothesis Sigma-Prikry Closed coloring Ascent Path Antichain HOD Constructible Universe AIM forcing weak diamond Subnormal ideal Strongly compact cardinal Absoluteness tensor product graph Almost-disjoint family strongly bounded groups Martin's Axiom Diamond Subtle tree property projective Boolean algebra full tree Fast club regressive Souslin tree Monotonically far Luzin set Reflecting stationary set Knaster Iterated forcing Cardinal Invariants Local Club Condensation. Well-behaved magma perfectly normal Universal Sequences weak square GMA Hereditarily Lindelöf space Lipschitz reduction L-space Entangled linear order Foundations middle diamond Ramsey theory over partitions reflection principles C-sequence Diamond-sharp Partition relations for trees Chromatic number incompactness weak Kurepa tree stationary reflection Poset Axiom R free Boolean algebra Nonspecial tree Amenable C-sequence Kurepa Hypothesis Erdos Cardinal transformations Sakurai's Bell inequality diamond star Weakly compact cardinal SNR Dowker space Was Ulam right? indecomposable filter Subadditive club_AD Rock n' Roll Commutative cancellative semigroups Almost countably chromatic S-Space positive partition relation Diamond for trees Dushnik-Miller Ineffable cardinal Distributive tree Strongly Luzin set ccc Vanishing levels Knaster and friends Singular Density stationary hitting 54G20 specializable Souslin tree Aronszajn tree polarized partition relation Ulam matrix Generalized Clubs Uniformly coherent very good scale Small forcing PFA Chang's conjecture Forcing Axioms Successor of Singular Cardinal Prevalent singular cardinals Prikry-type forcing ZFC construction Selective Ultrafilter nonmeager set
Tag Archives: Amenable C-sequence
Winter School in Abstract Analysis, January 2023
I gave a 3-lecture tutorial at the Winter School in Abstract Analysis in Steken, January 2023. Title: Club guessing Abstract. Club guessing principles were introduced by Shelah as a weakening of Jensen’s diamond. Most spectacularly, they were used to prove … Continue reading
Was Ulam right? I: Basic theory and subnormal ideals
Joint work with Tanmay Inamdar. Abstract. We introduce various coloring principles which generalize the so-called onto mapping principle of Sierpinski to larger cardinals and general ideals. We prove that these principles capture the notion of an Ulam matrix and allow … Continue reading
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
