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