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O-space very good scale Ramsey theory over partitions Forcing Ulam matrix Subtle tree property Interval topology on trees ZFC construction club_AD Local Club Condensation. Amenable C-sequence Generalized descriptive set theory Strongly compact cardinal Sigma-Prikry Ascending path Well-behaved magma Commutative cancellative semigroups Singular cofinality Sierpinski's onto mapping principle Subtle cardinal Fat stationary set countably metacompact ccc Filter reflection Antichain diamond star Erdos-Hajnal graphs free Souslin tree Vanishing levels Uniformly homogeneous Fodor-type reflection transformations Almost Souslin projective Boolean algebra positive partition relation Forcing with side conditions Distributive tree Chromatic number Weakly compact cardinal Reduced Power Almost-disjoint family Knaster Singular Density HOD Shelah's Strong Hypothesis 54G20 Large Cardinals square Erdos Cardinal Hindman's Theorem tensor product graph Whitehead Problem Aronszajn tree Precaliber stationary hitting Rado's conjecture Foundations Closed coloring AIM forcing Chang's conjecture Small forcing stick super-Souslin tree Countryman line Forcing Axioms Ostaszewski square Respecting tree Non-saturation coloring number xbox SNR Dushnik-Miller middle diamond P-Ideal Dichotomy Dowker space Strongly Luzin set Singular cardinals combinatorics Martin's Axiom regressive Souslin tree full tree Greatly Mahlo Kurepa Hypothesis Hedetniemi's conjecture higher Baire space free Boolean algebra S-Space indecomposable filter L-space Subnormal ideal Strong coloring Postprocessing function Prevalent singular cardinals b-scale Sakurai's Bell inequality Subadditive Diamond Slim tree strongly bounded groups Coherent tree square principles unbounded function Ascent Path weak Kurepa tree Open Access Prikry-type forcing C-sequence Souslin Tree Square-Brackets Partition Relations approachability ideal Cardinal function Rock n' Roll Axiom R polarized partition relation Selective Ultrafilter Universal Sequences Club Guessing Reflecting stationary set Ineffable cardinal Uniformly coherent Hereditarily Lindelöf space incompactness Successor of Singular Cardinal weak square Constructible Universe Cohen real Was Ulam right? Nonspecial tree stationary reflection perfectly normal Partition Relations Diamond for trees Diamond-sharp Knaster and friends Fast club Absoluteness Poset Lipschitz reduction Analytic sets nonmeager set Intersection model PFA(S)[S] Commutative projection system OCA GMA Generalized Clubs Almost countably chromatic Parameterized proxy principle Minimal Walks weak diamond sap Rainbow sets Monotonically far specializable Souslin tree Uniformization Luzin set reflection principles Mandelbrot set PFA Cardinal Invariants Successor of Regular Cardinal Iterated forcing Microscopic Approach Jonsson cardinal Entangled linear order
Tag Archives: 20A15
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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