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