Archives
Keywords
Generalized descriptive set theory Iterated forcing Cohen real projective Boolean algebra super-Souslin tree Singular cofinality Uniformly homogeneous reflection principles Axiom R Erdos Cardinal Knaster and friends positive partition relation Antichain Almost Souslin stationary hitting Nonspecial tree PFA Weakly compact cardinal Diamond-sharp S-Space Chang's conjecture stick Partition Relations specializable Souslin tree Minimal Walks Ostaszewski square Parameterized proxy principle Commutative cancellative semigroups AIM forcing xbox P-Ideal Dichotomy square club_AD weak diamond Coherent tree Hedetniemi's conjecture Hereditarily Lindelöf space Diamond for trees b-scale OCA Prikry-type forcing Subtle cardinal Well-behaved magma SNR polarized partition relation free Souslin tree diamond star Luzin set Selective Ultrafilter Singular cardinals combinatorics full tree unbounded function Lipschitz reduction Small forcing strongly bounded groups Constructible Universe Singular Density incompactness Cardinal Invariants Strongly Luzin set Ulam matrix ccc sap Club Guessing Dowker space Cardinal function Diamond Sierpinski's onto mapping principle indecomposable ultrafilter Rock n' Roll Knaster Microscopic Approach Slim tree ZFC construction Poset Analytic sets Universal Sequences Subnormal ideal coloring number Sigma-Prikry Successor of Regular Cardinal Absoluteness Fast club Forcing Axioms approachability ideal Jonsson cardinal Generalized Clubs Aronszajn tree Large Cardinals stationary reflection Whitehead Problem Non-saturation Was Ulam right C-sequence GMA weak square Erdos-Hajnal graphs Fodor-type reflection Sakurai's Bell inequality middle diamond Closed coloring Hindman's Theorem square principles Local Club Condensation. Uniformly coherent Forcing transformations Rainbow sets Chromatic number Subadditive Successor of Singular Cardinal tensor product graph Almost countably chromatic Filter reflection L-space HOD countably metacompact Martin's Axiom Mandelbrot set weak Kurepa tree Square-Brackets Partition Relations Prevalent singular cardinals very good scale Almost-disjoint family Foundations free Boolean algebra nonmeager set Fat stationary set Strong coloring Ascent Path higher Baire space Postprocessing function Ineffable cardinal O-space Subtle tree property Shelah's Strong Hypothesis Ramsey theory over partitions regressive Souslin tree Vanishing levels Kurepa Hypothesis 54G20 Amenable C-sequence Souslin Tree Precaliber Distributive tree Rado's conjecture Reflecting stationary set Uniformization PFA(S)[S] Dushnik-Miller Greatly Mahlo Reduced Power Open Access
Tag Archives: 03E75
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
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, Erdos Cardinal, Hindman's Theorem, Jonsson cardinal, Kurepa Hypothesis, Square-Brackets Partition Relations, Weakly compact cardinal, ZFC construction
1 Comment
Hedetniemi’s conjecture for uncountable graphs
Abstract. It is proved that in Godel’s constructible universe, for every successor cardinal $\kappa$, there exist graphs $\mathcal G$ and $\mathcal H$ of size and chromatic number $\kappa$, for which the tensor product graph $\mathcal G\times\mathcal H$ is countably chromatic. … Continue reading
Openly generated Boolean algebras and the Fodor-type reflection principle
Joint work with Sakaé Fuchino. Abstract: We prove that the Fodor-type Reflection Principle (FRP) is equivalent to the assertion that any Boolean algebra is openly generated if and only if it is $\aleph _2$-projective. Previously it was known that this … Continue reading
