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AIM forcing Partition Relations square principles S-Space SNR Chromatic number OCA xbox PFA transformations positive partition relation Coherent tree sap Well-behaved magma indecomposable filter HOD Nonspecial tree Ineffable cardinal Shelah's Strong Hypothesis very good scale Sakurai's Bell inequality Singular cofinality Club Guessing Subadditive Poset reflection principles Diamond-sharp b-scale Subtle cardinal Knaster Slim tree ZFC construction Strongly Luzin set Fat stationary set Ascending path Generalized descriptive set theory Sierpinski's onto mapping principle Cardinal function Erdos Cardinal Fodor-type reflection Erdos-Hajnal graphs Absoluteness Singular cardinals combinatorics approachability ideal Rado's conjecture Knaster and friends Martin's Axiom Universal Sequences Postprocessing function Forcing Axioms super-Souslin tree Jonsson cardinal Cohen real Ascent Path perfectly normal middle diamond Forcing Prevalent singular cardinals Fast club Cardinal Invariants Uniformly homogeneous Souslin Tree Precaliber Minimal Walks nonmeager set Strong coloring weak Kurepa tree square ccc specializable Souslin tree Constructible Universe Amenable C-sequence Dowker space Almost countably chromatic Ramsey theory over partitions Strongly compact cardinal Axiom R unbounded function Intersection model Hindman's Theorem Commutative projection system Interval topology on trees Ulam matrix club_AD PFA(S)[S] Monotonically far Open Access Foundations Aronszajn tree C-sequence stick Almost-disjoint family Reduced Power L-space Selective Ultrafilter Hereditarily Lindelöf space Chang's conjecture free Boolean algebra Analytic sets incompactness Parameterized proxy principle Entangled linear order polarized partition relation Luzin set Kurepa Hypothesis Microscopic Approach Filter reflection Weakly compact cardinal Uniformly coherent Subnormal ideal stationary reflection weak diamond Successor of Regular Cardinal Was Ulam right? stationary hitting Dushnik-Miller strongly bounded groups Vanishing levels free Souslin tree Prikry-type forcing Local Club Condensation. Partition relations for trees O-space Subtle tree property Iterated forcing Singular Density Diamond for trees projective Boolean algebra weak square Rainbow sets Sigma-Prikry Successor of Singular Cardinal Large Cardinals Generalized Clubs Commutative cancellative semigroups countably metacompact Distributive tree regressive Souslin tree Uniformization Antichain coloring number Mandelbrot set full tree Ostaszewski square Reflecting stationary set Lipschitz reduction Forcing with side conditions Almost Souslin Greatly Mahlo P-Ideal Dichotomy Hedetniemi's conjecture higher Baire space Closed coloring Diamond Non-saturation Square-Brackets Partition Relations diamond star Respecting tree Rock n' Roll Whitehead Problem Small forcing 54G20 GMA Countryman line tensor product graph
Tag Archives: 20F06
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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