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