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