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