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### Recent blog posts

- Prikry forcing may add a Souslin tree June 12, 2016
- The reflection principle $R_2$ May 20, 2016
- Prolific Souslin trees March 17, 2016
- Generalizations of Martin’s Axiom and the well-met condition January 11, 2015
- Many diamonds from just one January 6, 2015
- Happy new jewish year! September 24, 2014
- Square principles April 19, 2014
- Partitioning the club guessing January 22, 2014

### Keywords

20M14 Prikry-type forcing xbox Parameterized proxy principle Forcing Axioms Chang's conjecture Singular Cofinality Aronszajn tree Chromatic number ccc Kurepa Hypothesis Club Guessing Knaster PFA(S)[S] Souslin Tree Reduced Power b-scale Generalized Clubs OCA Non-saturation Square-Brackets Partition Relations Stevo Todorcevic stationary hitting square principles Sakurai's Bell inequality 05A17 Dushnik-Miller very good scale P-Ideal Dichotomy Uniformization Successor of Singular Cardinal Almost Souslin diamond star reflection principles Diamond Foundations Erdos-Hajnal graphs Commutative cancellative semigroups Hedetniemi's conjecture Poset Singular cardinals combinatorics tensor product graph Rainbow sets HOD Cardinal function Rock n' Roll weak diamond middle diamond Hereditarily Lindelöf space Coherent tree square PFA Mandelbrot set Singular coﬁnality Almost countably chromatic Large Cardinals projective Boolean algebra Fodor-type reflection 11P99 Universal Sequences Slim tree L-space Jonsson cardinal Shelah's Strong Hypothesis Rado's conjecture coloring number S-Space Almost-disjoint famiy incompactness Hindman's Theorem Small forcing Partition Relations Martin's Axiom Weakly compact cardinal approachability ideal Erdos Cardinal Singular Density Absoluteness polarized partition relation sap Selective Ultrafilter 05D10 Successor of Regular Cardinal Prevalent singular cardinals Fast club Cardinal Invariants Forcing Antichain Ascent Path Cohen real free Boolean algebra Whitehead Problem Constructible Universe Axiom R stationary reflection Ostaszewski square Fat stationary set weak square Minimal Walks Microscopic Approach

# Tag Archives: coloring number

## 2017 Workshop in Set Theory, Oberwolfach

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