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