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