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