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