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