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