Archives
Keywords
Subtle tree property Antichain Cardinal Invariants free Boolean algebra ccc Distributive tree SNR HOD Subnormal ideal free Souslin tree Analytic sets Chang's conjecture Chromatic number Universal Sequences Cardinal function Weakly compact cardinal Microscopic Approach very good scale L-space GMA Diamond for trees Singular cofinality Strongly Luzin set Uniformization nonmeager set Dowker space stationary hitting Constructible Universe unbounded function Sakurai's Bell inequality Was Ulam right? Almost Souslin Entangled linear order strongly bounded groups Selective Ultrafilter Diamond stationary reflection Shelah's Strong Hypothesis Local Club Condensation. Cohen real Prevalent singular cardinals Respecting tree Minimal Walks square principles Rock n' Roll Ulam matrix projective Boolean algebra Sierpinski's onto mapping principle ZFC construction indecomposable filter Large Cardinals approachability ideal Poset Prikry-type forcing positive partition relation Subadditive Almost-disjoint family Ramsey theory over partitions Martin's Axiom Forcing Absoluteness Fodor-type reflection higher Baire space Knaster and friends Rainbow sets Ostaszewski square Ascent Path full tree Generalized Clubs Forcing Axioms transformations Closed coloring Strongly compact cardinal Mandelbrot set specializable Souslin tree weak diamond C-sequence Vanishing levels Square-Brackets Partition Relations Almost countably chromatic Precaliber Parameterized proxy principle diamond star Interval topology on trees super-Souslin tree O-space countably metacompact Rado's conjecture S-Space Generalized descriptive set theory Aronszajn tree Ineffable cardinal weak square Fat stationary set Erdos-Hajnal graphs reflection principles Iterated forcing Subtle cardinal Hindman's Theorem incompactness Reduced Power Diamond-sharp middle diamond Monotonically far Successor of Singular Cardinal Slim tree Strong coloring P-Ideal Dichotomy Commutative cancellative semigroups Club Guessing Sigma-Prikry sap regressive Souslin tree Greatly Mahlo square Dushnik-Miller Ascending path Uniformly coherent Souslin Tree Jonsson cardinal OCA Commutative projection system Postprocessing function PFA(S)[S] Intersection model b-scale perfectly normal Partition Relations Coherent tree coloring number PFA Countryman line Whitehead Problem xbox Uniformly homogeneous Well-behaved magma Foundations Reflecting stationary set Small forcing Non-saturation Hedetniemi's conjecture Nonspecial tree tensor product graph Knaster club_AD Kurepa Hypothesis Singular Density Amenable C-sequence Forcing with side conditions 54G20 stick Filter reflection weak Kurepa tree Fast club Axiom R Erdos Cardinal Hereditarily Lindelöf space Successor of Regular Cardinal Luzin set Open Access AIM forcing Singular cardinals combinatorics polarized partition relation Lipschitz reduction
Category Archives: Groups
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
Sums of triples in Abelian groups
Joint work with Ido Feldman. Abstract. Motivated by a problem in additive Ramsey theory, we extend Todorcevic’s partitions of three-dimensional combinatorial cubes to handle additional three-dimensional objects. As a corollary, we get that if the continuum hypothesis fails, then for … Continue reading
Strong failures of higher analogs of Hindman’s Theorem
Joint work with David J. Fernández Bretón. Abstract. We show that various analogs of Hindman’s Theorem fail in a strong sense when one attempts to obtain uncountable monochromatic sets: Theorem 1. There exists a colouring $c:\mathbb R\rightarrow\mathbb Q$, such that … Continue reading
Posted in Groups, Partition Relations, Publications
Tagged 03E02, 03E35, 03E75, 05A17, 05D10, 11P99, 20M14, Chang's conjecture, Commutative cancellative semigroups, Entangled linear order, Erdos Cardinal, Hindman's Theorem, Jonsson cardinal, Kurepa Hypothesis, Square-Brackets Partition Relations, Weakly compact cardinal, ZFC construction
1 Comment
