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