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