Archives
Keywords
Singular cardinals combinatorics Mandelbrot set Ascending path Subadditive Coherent tree Fodor-type reflection stick very good scale weak Kurepa tree Aronszajn tree Antichain Small forcing square Monotonically far Cohen real C-sequence Nonspecial tree Uniformly homogeneous super-Souslin tree Successor of Regular Cardinal Whitehead Problem Knaster higher Baire space countably metacompact Rock n' Roll approachability ideal SNR Non-saturation Postprocessing function Erdos-Hajnal graphs full tree Cardinal function b-scale xbox Uniformization GMA PFA Souslin Tree Singular cofinality HOD strongly bounded groups Poset Kurepa Hypothesis Shelah's Strong Hypothesis Jonsson cardinal Entangled linear order Chromatic number Respecting tree Commutative projection system Subnormal ideal weak diamond Prevalent singular cardinals Forcing Axioms Hedetniemi's conjecture weak square Intersection model Singular Density reflection principles Forcing with side conditions Ascent Path Greatly Mahlo Constructible Universe regressive Souslin tree Subtle cardinal Erdos Cardinal P-Ideal Dichotomy stationary reflection Prikry-type forcing stationary hitting Local Club Condensation. L-space free Souslin tree middle diamond club_AD Strong coloring Fast club S-Space O-space Foundations Absoluteness Analytic sets Hindman's Theorem Strongly compact cardinal Lipschitz reduction Large Cardinals Forcing ccc Amenable C-sequence Diamond for trees Hereditarily Lindelöf space Diamond-sharp Martin's Axiom Diamond ZFC construction Countryman line Filter reflection Reduced Power AIM forcing free Boolean algebra unbounded function Chang's conjecture Uniformly coherent Parameterized proxy principle Generalized Clubs Cardinal Invariants 54G20 sap Fat stationary set tensor product graph polarized partition relation Almost countably chromatic Microscopic Approach Minimal Walks Club Guessing Rainbow sets Dushnik-Miller Distributive tree Open Access Strongly Luzin set transformations positive partition relation Was Ulam right? Partition Relations Closed coloring Square-Brackets Partition Relations Almost-disjoint family Axiom R Knaster and friends Ineffable cardinal indecomposable filter Sigma-Prikry Interval topology on trees specializable Souslin tree Reflecting stationary set Ostaszewski square Subtle tree property Dowker space Successor of Singular Cardinal projective Boolean algebra Commutative cancellative semigroups Ulam matrix Almost Souslin Well-behaved magma Luzin set Precaliber Rado's conjecture Generalized descriptive set theory Sierpinski's onto mapping principle Selective Ultrafilter Vanishing levels OCA PFA(S)[S] square principles nonmeager set coloring number Weakly compact cardinal incompactness Slim tree Sakurai's Bell inequality Iterated forcing Universal Sequences Ramsey theory over partitions perfectly normal diamond star
Tag Archives: 05C15
Reflection on the coloring and chromatic numbers
Joint work with Chris Lambie-Hanson. Abstract. We prove that reflection of the coloring number of graphs is consistent with non-reflection of the chromatic number. Moreover, it is proved that incompactness for the chromatic number of graphs (with arbitrarily large gaps) … Continue reading
Posted in Compactness, Infinite Graphs, Publications
Tagged 03E35, 05C15, 05C63, Chang's conjecture, Chromatic number, coloring number, Fodor-type reflection, incompactness, Iterated forcing, Parameterized proxy principle, Postprocessing function, Rado's conjecture, square, stationary reflection
2 Comments
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
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
Chromatic numbers of graphs – large gaps
Abstract. We say that a graph $G$ is $(\aleph_0,\kappa)$-chromatic if $\text{Chr}(G)=\kappa$, while $\text{Chr}(G’)\le\aleph_0$ for any subgraph $G’$ of $G$ of size $<|G|$. The main result of this paper reads as follows. If $\square_\lambda+\text{CH}_\lambda$ holds for a given uncountable cardinal $\lambda$, … Continue reading
Posted in Compactness, Infinite Graphs, Publications
Tagged 03E35, 05C15, 05C63, Almost countably chromatic, Chromatic number, incompactness, Ostaszewski square
6 Comments
