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Absoluteness Diamond for trees HOD Entangled linear order countably metacompact Respecting tree Erdos Cardinal b-scale P-Ideal Dichotomy Ascending path Fodor-type reflection diamond star Fast club Nonspecial tree Closed coloring Poset Strongly Luzin set Analytic sets Prevalent singular cardinals Subnormal ideal coloring number Reflecting stationary set Diamond-sharp polarized partition relation Uniformly homogeneous Successor of Regular Cardinal stationary hitting Whitehead Problem transformations Strong coloring Constructible Universe reflection principles Lipschitz reduction perfectly normal weak square incompactness Uniformization Reduced Power Singular Density Club Guessing C-sequence Dushnik-Miller L-space Chromatic number Was Ulam right? Shelah's Strong Hypothesis very good scale club_AD PFA(S)[S] tensor product graph AIM forcing Partition relations for trees Fat stationary set Local Club Condensation. stationary reflection Prikry-type forcing Vanishing levels Large Cardinals Cardinal function Erdos-Hajnal graphs Rainbow sets Sigma-Prikry Ulam matrix Rock n' Roll indecomposable filter Intersection model Well-behaved magma Greatly Mahlo Subadditive projective Boolean algebra Non-saturation Dowker space Distributive tree Hereditarily Lindelöf space nonmeager set Forcing with side conditions Countryman line Precaliber Ostaszewski square Strongly compact cardinal Slim tree xbox Mandelbrot set Generalized descriptive set theory square principles sap Sierpinski's onto mapping principle Souslin Tree positive partition relation Foundations approachability ideal Almost Souslin specializable Souslin tree Partition Relations Hedetniemi's conjecture Sakurai's Bell inequality Minimal Walks strongly bounded groups Singular cardinals combinatorics Diamond 54G20 weak Kurepa tree regressive Souslin tree middle diamond Almost-disjoint family PFA Uniformly coherent Parameterized proxy principle weak diamond Postprocessing function Jonsson cardinal higher Baire space Microscopic Approach Iterated forcing Monotonically far Selective Ultrafilter Axiom R Chang's conjecture Weakly compact cardinal Small forcing Open Access Kurepa Hypothesis Aronszajn tree ccc Ascent Path Forcing Axioms S-Space stick OCA SNR Coherent tree super-Souslin tree Luzin set unbounded function Antichain free Souslin tree free Boolean algebra Commutative projection system Subtle tree property Amenable C-sequence Forcing GMA Singular cofinality Commutative cancellative semigroups Universal Sequences Ineffable cardinal Cardinal Invariants square Successor of Singular Cardinal Generalized Clubs Rado's conjecture O-space Martin's Axiom Filter reflection Knaster and friends Hindman's Theorem Almost countably chromatic Subtle cardinal Square-Brackets Partition Relations Ramsey theory over partitions full tree ZFC construction Interval topology on trees Cohen real Knaster
Category Archives: Groups
A Shelah group in ZFC
Joint work with Márk Poór. Abstract. In a paper from 1980, Shelah constructed an uncountable group all of whose proper subgroups are countable. Assuming the continuum hypothesis, he constructed an uncountable group $G$ that moreover admits an integer $n$ satisfying … Continue reading
Posted in Groups, Publications
Tagged 03E02, 03E75, 20A15, 20E15, 20F06, Jonsson cardinal, Open Access, Strong coloring, strongly bounded groups, Subadditive, ZFC construction
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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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