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