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