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