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