Archives
Keywords
Prevalent singular cardinals Uniformly coherent Shelah's Strong Hypothesis polarized partition relation Minimal Walks Absoluteness Martin's Axiom nonmeager set Filter reflection higher Baire space Axiom R Lipschitz reduction super-Souslin tree Greatly Mahlo Forcing Axioms Rock n' Roll Subnormal ideal Singular Density Ramsey theory over partitions Diamond-sharp indecomposable ultrafilter square principles Mandelbrot set Open Access S-Space Uniformization Antichain Generalized descriptive set theory Non-saturation Almost Souslin Ascent Path Subtle tree property 54G20 Amenable C-sequence positive partition relation O-space Knaster Singular cofinality unbounded function Hindman's Theorem Rainbow sets Subtle cardinal SNR Parameterized proxy principle free Souslin tree Luzin set Sierpinski's onto mapping principle free Boolean algebra Rado's conjecture Uniformly homogeneous Chromatic number transformations Local Club Condensation. Selective Ultrafilter Fodor-type reflection coloring number Poset Diamond for trees HOD Whitehead Problem Subadditive approachability ideal Aronszajn tree Cohen real diamond star Generalized Clubs Ostaszewski square P-Ideal Dichotomy stick Fast club Sigma-Prikry Almost-disjoint family Constructible Universe Well-behaved magma full tree Square-Brackets Partition Relations Slim tree incompactness Iterated forcing strongly bounded groups Club Guessing Dowker space Singular cardinals combinatorics weak diamond stationary hitting Large Cardinals Analytic sets Ineffable cardinal Nonspecial tree Precaliber ccc stationary reflection regressive Souslin tree PFA(S)[S] Knaster and friends Postprocessing function middle diamond very good scale Reduced Power ZFC construction specializable Souslin tree Vanishing levels PFA Partition Relations Small forcing Cardinal function Jonsson cardinal C-sequence reflection principles Was Ulam right Erdos-Hajnal graphs OCA Almost countably chromatic Successor of Regular Cardinal Prikry-type forcing Coherent tree projective Boolean algebra Fat stationary set AIM forcing Strongly Luzin set Chang's conjecture weak Kurepa tree L-space club_AD Strong coloring Kurepa Hypothesis GMA Forcing Souslin Tree Hedetniemi's conjecture Reflecting stationary set Closed coloring countably metacompact tensor product graph Sakurai's Bell inequality weak square Hereditarily Lindelöf space sap Diamond b-scale Foundations Cardinal Invariants Weakly compact cardinal Successor of Singular Cardinal Erdos Cardinal square Microscopic Approach Dushnik-Miller xbox Ulam matrix Commutative cancellative semigroups Universal Sequences Distributive tree
Tag Archives: Ostaszewski square
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
The Ostaszewski square, and homogeneous Souslin trees
Abstract: Assume GCH and let $\lambda$ denote an uncountable cardinal. We prove that if $\square_\lambda$ holds, then this may be witnessed by a coherent sequence $\left\langle C_\alpha \mid \alpha<\lambda^+\right\rangle$ with the following remarkable guessing property: For every sequence $\langle A_i\mid i<\lambda\rangle$ … Continue reading
Posted in Publications, Souslin Hypothesis, Squares and Diamonds
Tagged 03E05, 03E35, Club Guessing, Fat stationary set, Ostaszewski square, Souslin Tree
5 Comments
