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