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