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