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Interval topology on trees stationary hitting Rado's conjecture Lipschitz reduction incompactness Uniformization club_AD Dowker space Selective Ultrafilter Almost countably chromatic approachability ideal Generalized descriptive set theory Generalized Clubs Reduced Power Fast club Partition Relations Strongly compact cardinal Large Cardinals Open Access weak diamond ZFC construction Fodor-type reflection Kurepa Hypothesis Erdos Cardinal regressive Souslin tree Parameterized proxy principle Coherent tree Constructible Universe Hereditarily Lindelöf space weak square strongly bounded groups unbounded function Cohen real PFA(S)[S] perfectly normal Strongly Luzin set Small forcing Strong coloring specializable Souslin tree weak Kurepa tree Ineffable cardinal Intersection model Non-saturation Entangled linear order Subnormal ideal Subadditive Foundations 54G20 Aronszajn tree Cardinal function Prikry-type forcing Diamond for trees Club Guessing Well-behaved magma stationary reflection Ascent Path Sigma-Prikry Slim tree Diamond-sharp PFA Antichain higher Baire space Almost Souslin free Boolean algebra square Rock n' Roll Martin's Axiom Uniformly homogeneous L-space Shelah's Strong Hypothesis free Souslin tree Was Ulam right? Iterated forcing C-sequence Microscopic Approach Axiom R Precaliber Amenable C-sequence very good scale Luzin set coloring number diamond star stick tensor product graph Whitehead Problem Singular Density reflection principles O-space Erdos-Hajnal graphs Local Club Condensation. Vanishing levels Respecting tree Commutative projection system Closed coloring polarized partition relation Successor of Singular Cardinal Hindman's Theorem Reflecting stationary set Sierpinski's onto mapping principle Square-Brackets Partition Relations S-Space P-Ideal Dichotomy Chromatic number Partition relations for trees xbox b-scale Ramsey theory over partitions Poset Ostaszewski square GMA Singular cofinality Subtle tree property Monotonically far Jonsson cardinal Prevalent singular cardinals Analytic sets projective Boolean algebra Souslin Tree middle diamond Minimal Walks Uniformly coherent Forcing with side conditions Chang's conjecture Forcing Axioms Almost-disjoint family Absoluteness Countryman line Diamond Knaster Weakly compact cardinal Subtle cardinal Commutative cancellative semigroups Ascending path Universal Sequences Knaster and friends Greatly Mahlo HOD Filter reflection Fat stationary set nonmeager set Dushnik-Miller full tree Successor of Regular Cardinal indecomposable filter square principles SNR countably metacompact OCA Cardinal Invariants Ulam matrix Mandelbrot set transformations Rainbow sets positive partition relation Postprocessing function sap super-Souslin tree Distributive tree AIM forcing Hedetniemi's conjecture ccc Singular cardinals combinatorics Forcing Sakurai's Bell inequality Nonspecial tree
Tag Archives: Erdos Cardinal
Strong failures of higher analogs of Hindman’s Theorem
Joint work with David J. Fernández Bretón. Abstract. We show that various analogs of Hindman’s Theorem fail in a strong sense when one attempts to obtain uncountable monochromatic sets: Theorem 1. There exists a colouring $c:\mathbb R\rightarrow\mathbb Q$, such that … Continue reading
Posted in Groups, Partition Relations, Publications
Tagged 03E02, 03E35, 03E75, 05A17, 05D10, 11P99, 20M14, Chang's conjecture, Commutative cancellative semigroups, Entangled linear order, Erdos Cardinal, Hindman's Theorem, Jonsson cardinal, Kurepa Hypothesis, Square-Brackets Partition Relations, Weakly compact cardinal, ZFC construction
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A large cardinal in the constructible universe
In this post, we shall provide a proof of Silver’s theorem that the Erdos caridnal $\kappa(\omega)$ relativizes to Godel’s constructible universe. First, recall some definitions. Given a function $f:[\kappa]^{<\omega}\rightarrow \mu$, we say that $I\subseteq\kappa$ is a set of indiscernibles for … Continue reading
