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Sakurai's Bell inequality Erdos Cardinal Foundations Generalized descriptive set theory Mandelbrot set Reduced Power Rado's conjecture stationary reflection Ramsey theory over partitions Fat stationary set Postprocessing function Distributive tree Absoluteness tensor product graph Ostaszewski square Sierpinski's onto mapping principle reflection principles Uniformly coherent Slim tree xbox polarized partition relation Martin's Axiom S-Space Non-saturation free Boolean algebra Square-Brackets Partition Relations Aronszajn tree PFA Uniformly homogeneous Poset club_AD Cardinal function strongly bounded groups Antichain Subnormal ideal Filter reflection Knaster and friends Subtle tree property L-space stick Prikry-type forcing Singular cofinality Subtle cardinal Luzin set OCA Strongly Luzin set Generalized Clubs Universal Sequences Greatly Mahlo Was Ulam right positive partition relation Hedetniemi's conjecture Shelah's Strong Hypothesis ZFC construction Cohen real full tree Weakly compact cardinal Prevalent singular cardinals Forcing Axioms Cardinal Invariants stationary hitting Successor of Singular Cardinal Coherent tree unbounded function O-space Analytic sets coloring number Closed coloring Successor of Regular Cardinal Forcing Diamond for trees Iterated forcing regressive Souslin tree Chang's conjecture free Souslin tree very good scale C-sequence transformations super-Souslin tree diamond star incompactness Selective Ultrafilter weak square Parameterized proxy principle Rainbow sets Hindman's Theorem weak Kurepa tree Local Club Condensation. middle diamond Small forcing Jonsson cardinal indecomposable ultrafilter Axiom R Kurepa Hypothesis Nonspecial tree Reflecting stationary set Whitehead Problem Ulam matrix Uniformization Dowker space Club Guessing Open Access Amenable C-sequence Well-behaved magma Precaliber ccc PFA(S)[S] Ascent Path b-scale Hereditarily Lindelöf space weak diamond AIM forcing Partition Relations Diamond Lipschitz reduction Singular Density Knaster Large Cardinals Minimal Walks higher Baire space Microscopic Approach Singular cardinals combinatorics Fodor-type reflection approachability ideal Sigma-Prikry countably metacompact specializable Souslin tree HOD projective Boolean algebra nonmeager set square principles sap P-Ideal Dichotomy Diamond-sharp square SNR Subadditive Vanishing levels Strong coloring Chromatic number Commutative cancellative semigroups Constructible Universe Almost countably chromatic Souslin Tree 54G20 Almost-disjoint family Ineffable cardinal Almost Souslin Fast club Erdos-Hajnal graphs Rock n' Roll Dushnik-Miller GMA
Tag Archives: incompactness
11th Young Set Theory Workshop, June 2018
I gave a 4-lecture tutorial at the 11th Young Set Theory Workshop, Lausanne, June 2018. Title: In praise of C-sequences. Abstract. Ulam and Solovay showed that any stationary set may be split into two. Is it also the case that … Continue reading
Posted in Invited Talks
Tagged Aronszajn tree, C-sequence, incompactness, Knaster, Minimal Walks, Postprocessing function, square
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MFO workshop in Set Theory, February 2017
I gave an invited talk at the Set Theory workshop in Obwerwolfach, February 2017. Talk Title: Coloring vs. Chromatic. Abstract: In a joint work with Chris Lambie-Hanson, we study the interaction between compactness for the chromatic number (of graphs) and … Continue reading
Posted in Invited Talks
Tagged Chromatic number, coloring number, incompactness, stationary reflection
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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
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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
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