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very good scale Almost countably chromatic Fodor-type reflection Lipschitz reduction Minimal Walks Subadditive Postprocessing function transformations Sakurai's Bell inequality PFA weak Kurepa tree Almost-disjoint family reflection principles Aronszajn tree Prikry-type forcing stick Reflecting stationary set Ascending path Coherent tree Vanishing levels Hedetniemi's conjecture Intersection model Partition Relations S-Space Subnormal ideal Strongly Luzin set Square-Brackets Partition Relations Countryman line full tree Axiom R Mandelbrot set C-sequence Ostaszewski square Souslin Tree AIM forcing projective Boolean algebra Ulam matrix Cardinal function Kurepa Hypothesis HOD Greatly Mahlo Amenable C-sequence Erdos-Hajnal graphs Rock n' Roll b-scale Rainbow sets Was Ulam right? Poset Luzin set Strong coloring GMA Jonsson cardinal Selective Ultrafilter Slim tree Uniformly homogeneous Dowker space Cardinal Invariants sap Club Guessing higher Baire space Forcing with side conditions Subtle cardinal Generalized descriptive set theory Baumgartner's square square principles Nonspecial tree Dushnik-Miller OCA strongly bounded groups Cohen real free Souslin tree Forcing Axioms Small forcing Erdos Cardinal polarized partition relation regressive Souslin tree weak square Universal Sequences Distributive tree Antichain Commutative projection system Respecting tree countably metacompact Ascent Path O-space Strongly compact cardinal Hindman's Theorem Filter reflection Prevalent singular cardinals Chang's conjecture Subtle tree property Precaliber stationary hitting Ineffable cardinal free Boolean algebra Singular Density unbounded function Sierpinski's onto mapping principle Rado's conjecture coloring number Interval topology on trees Fast club Shelah's Strong Hypothesis super-Souslin tree Sigma-Prikry Generalized Clubs Monotonically far Uniformly coherent stationary reflection Diamond for trees L-space Commutative cancellative semigroups Ramsey theory over partitions weak diamond SNR Whitehead Problem Almost Souslin Open Access specializable Souslin tree Successor of Regular Cardinal Entangled linear order Iterated forcing approachability ideal Large Cardinals ccc Singular cofinality incompactness middle diamond club_AD Successor of Singular Cardinal Forcing Partition relations for trees Constructible Universe Knaster and friends Analytic sets Microscopic Approach PFA(S)[S] tensor product graph Chromatic number Local Club Condensation. ZFC construction Fat stationary set indecomposable filter Non-saturation diamond star Weakly compact cardinal Parameterized proxy principle Absoluteness nonmeager set Well-behaved magma Knaster square positive partition relation Reduced Power Foundations Martin's Axiom 54G20 xbox Diamond Uniformization Singular cardinals combinatorics Closed coloring Diamond-sharp Hereditarily Lindelöf space P-Ideal Dichotomy perfectly normal
Tag Archives: 11P99
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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