Archives
Keywords
very good scale Aronszajn tree diamond star Distributive tree Monotonically far approachability ideal Knaster and friends Open Access Fat stationary set HOD Successor of Regular Cardinal Countryman line Small forcing specializable Souslin tree Club Guessing S-Space Reduced Power Partition relations for trees Coherent tree Cardinal function Fast club b-scale club_AD Cohen real Uniformly coherent Interval topology on trees square principles Sigma-Prikry polarized partition relation indecomposable filter Subadditive Antichain Ostaszewski square super-Souslin tree Cardinal Invariants Analytic sets projective Boolean algebra Subnormal ideal PFA Entangled linear order stationary reflection Commutative projection system Square-Brackets Partition Relations Weakly compact cardinal Almost countably chromatic Singular cardinals combinatorics weak diamond Whitehead Problem Fodor-type reflection Generalized Clubs Prikry-type forcing Subtle tree property Poset Diamond for trees Baumgartner's square Chromatic number positive partition relation OCA Erdos-Hajnal graphs Knaster GMA Uniformly homogeneous stick Ramsey theory over partitions Strongly compact cardinal Universal Sequences Was Ulam right? Hindman's Theorem AIM forcing Diamond Martin's Axiom Strongly Luzin set Non-saturation sap regressive Souslin tree Singular cofinality countably metacompact free Souslin tree Selective Ultrafilter Chang's conjecture Constructible Universe Postprocessing function Forcing with side conditions Local Club Condensation. xbox O-space weak Kurepa tree Strong coloring perfectly normal transformations square Lipschitz reduction Axiom R tensor product graph Greatly Mahlo Large Cardinals SNR Shelah's Strong Hypothesis Luzin set Ascending path L-space Mandelbrot set Almost Souslin Rock n' Roll Ascent Path Nonspecial tree Parameterized proxy principle reflection principles Diamond-sharp Commutative cancellative semigroups C-sequence Generalized descriptive set theory Partition Relations ccc Minimal Walks Kurepa Hypothesis free Boolean algebra Forcing Foundations incompactness Hereditarily Lindelöf space nonmeager set Ulam matrix Souslin Tree Hedetniemi's conjecture Almost-disjoint family Absoluteness 54G20 Vanishing levels Rado's conjecture Dushnik-Miller ZFC construction coloring number Singular Density Uniformization Prevalent singular cardinals Erdos Cardinal Rainbow sets unbounded function Well-behaved magma Respecting tree weak square Slim tree Sakurai's Bell inequality Successor of Singular Cardinal P-Ideal Dichotomy Sierpinski's onto mapping principle Precaliber higher Baire space Closed coloring Subtle cardinal strongly bounded groups Ineffable cardinal Filter reflection stationary hitting PFA(S)[S] Microscopic Approach full tree Amenable C-sequence Reflecting stationary set Intersection model Forcing Axioms Dowker space Iterated forcing Jonsson cardinal middle diamond
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, Publications
Tagged 03E02, 03E75, 20A15, 20E15, 20F06, Jonsson cardinal, Open Access, Strong coloring, strongly bounded groups, Subadditive, ZFC construction
3 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, Entangled linear order, 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
Posted in Compactness, Publications
Tagged 03E35, 03E55, 03E65, 03E75, 03G05, 06E05, Axiom R, Fodor-type reflection, free Boolean algebra, projective Boolean algebra, Shelah's Strong Hypothesis, stationary reflection
Comments Off on Openly generated Boolean algebras and the Fodor-type reflection principle
