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