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