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club_AD specializable Souslin tree Amenable C-sequence square Filter reflection Forcing Strong coloring Nonspecial tree higher Baire space free Boolean algebra Closed coloring b-scale Successor of Singular Cardinal Whitehead Problem Square-Brackets Partition Relations Reduced Power Ramsey theory over partitions Club Guessing Foundations Non-saturation tensor product graph positive partition relation diamond star strongly bounded groups Subnormal ideal Cardinal function Absoluteness Coherent tree Jonsson cardinal Greatly Mahlo Almost countably chromatic Chang's conjecture L-space xbox AIM forcing Poset polarized partition relation Subtle cardinal super-Souslin tree Lipschitz reduction Constructible Universe incompactness Cohen real Diamond-sharp Strongly Luzin set Weakly compact cardinal Fast club Luzin set Distributive tree Antichain Almost Souslin Small forcing Analytic sets PFA unbounded function Microscopic Approach weak diamond Diamond Uniformly coherent Shelah's Strong Hypothesis reflection principles Commutative cancellative semigroups Erdos-Hajnal graphs very good scale Cardinal Invariants free Souslin tree stick Singular cardinals combinatorics Diamond for trees Slim tree Reflecting stationary set Generalized descriptive set theory Ascent Path Hedetniemi's conjecture Aronszajn tree C-sequence ccc GMA Postprocessing function Ineffable cardinal Singular cofinality Rainbow sets Generalized Clubs Ostaszewski square Fodor-type reflection square principles indecomposable ultrafilter Vanishing levels Singular Density Sigma-Prikry Prikry-type forcing Partition Relations transformations Forcing Axioms Hindman's Theorem Subadditive Well-behaved magma Prevalent singular cardinals Rock n' Roll Minimal Walks Universal Sequences Large Cardinals Knaster and friends S-Space approachability ideal Knaster stationary reflection Open Access Was Ulam right countably metacompact middle diamond Uniformization Mandelbrot set regressive Souslin tree Rado's conjecture Dowker space P-Ideal Dichotomy 54G20 Local Club Condensation. weak Kurepa tree Sakurai's Bell inequality Erdos Cardinal ZFC construction PFA(S)[S] Almost-disjoint family Iterated forcing Kurepa Hypothesis Uniformly homogeneous Martin's Axiom Hereditarily Lindelöf space Souslin Tree Dushnik-Miller O-space Fat stationary set SNR OCA Parameterized proxy principle Subtle tree property Axiom R Precaliber full tree Selective Ultrafilter HOD projective Boolean algebra weak square coloring number Chromatic number sap nonmeager set stationary hitting Ulam matrix Sierpinski's onto mapping principle Successor of Regular Cardinal
Tag Archives: 20E15
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, Preprints
Tagged 03E02, 03E75, 20A15, 20E15, 20F06, Jonsson cardinal, Strong coloring, strongly bounded groups, Subadditive, ZFC construction
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