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