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