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