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