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