Archives
Keywords
Diamond for trees Microscopic Approach Chang's conjecture Generalized descriptive set theory Precaliber O-space PFA(S)[S] Subnormal ideal Sakurai's Bell inequality incompactness Whitehead Problem Almost-disjoint family Square-Brackets Partition Relations Hindman's Theorem Strongly compact cardinal polarized partition relation diamond star Sigma-Prikry Hereditarily Lindelöf space strongly bounded groups Knaster and friends HOD P-Ideal Dichotomy S-Space square principles Distributive tree Universal Sequences Forcing C-sequence Minimal Walks full tree Poset Luzin set ccc Singular Density Subtle tree property Weakly compact cardinal Diamond-sharp PFA Postprocessing function Fast club Ulam matrix sap ZFC construction Partition Relations Singular cardinals combinatorics weak diamond Sierpinski's onto mapping principle Commutative projection system projective Boolean algebra xbox Well-behaved magma stationary hitting Cardinal Invariants tensor product graph Uniformly coherent stationary reflection Singular cofinality Prevalent singular cardinals GMA Erdos Cardinal weak square Jonsson cardinal Ostaszewski square Kurepa Hypothesis Ramsey theory over partitions Constructible Universe approachability ideal Generalized Clubs Strongly Luzin set Aronszajn tree Souslin Tree Slim tree Axiom R Parameterized proxy principle Uniformly homogeneous Antichain Respecting tree SNR free Souslin tree Small forcing Open Access Filter reflection higher Baire space Almost countably chromatic Commutative cancellative semigroups 54G20 Coherent tree Rado's conjecture Strong coloring Club Guessing coloring number Closed coloring Erdos-Hajnal graphs Ineffable cardinal Uniformization Fodor-type reflection Iterated forcing Reduced Power specializable Souslin tree Amenable C-sequence Ascent Path Successor of Regular Cardinal OCA middle diamond free Boolean algebra stick b-scale Cardinal function very good scale positive partition relation Mandelbrot set Knaster unbounded function Absoluteness Diamond Lipschitz reduction Shelah's Strong Hypothesis Local Club Condensation. transformations reflection principles Vanishing levels Rainbow sets Martin's Axiom nonmeager set Almost Souslin Rock n' Roll indecomposable ultrafilter Foundations Subadditive Nonspecial tree club_AD Countryman line weak Kurepa tree Analytic sets Dowker space Large Cardinals Subtle cardinal Non-saturation super-Souslin tree Chromatic number Greatly Mahlo Cohen real Dushnik-Miller Intersection model Successor of Singular Cardinal Reflecting stationary set AIM forcing regressive Souslin tree Hedetniemi's conjecture countably metacompact Fat stationary set square Was Ulam right? Selective Ultrafilter Prikry-type forcing L-space Forcing Axioms
Tag Archives: Constructible Universe
Same Graph, Different Universe
Abstract. May the same graph admit two different chromatic numbers in two different universes? how about infinitely many different values? and can this be achieved without changing the cardinals structure? In this paper, it is proved that in Godel’s constructible … Continue reading
Posted in Infinite Graphs, Publications
Tagged 03E35, 05C15, 05C63, approachability ideal, Chromatic number, Constructible Universe, Forcing, Ostaszewski square
10 Comments
INFTY Final Conference, March 2014
I gave an invited talk at the INFTY Final Conference meeting, Bonn, March 4-7, 2014. [Curiosity: Georg Cantor was born March 3, 1845] Title: Same Graph, Different Universe. Abstract: In a paper from 1998, answering a question of Hajnal, Soukup … Continue reading
Hedetniemi’s conjecture for uncountable graphs
Abstract. It is proved that in Godel’s constructible universe, for every successor cardinal