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