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