### Archives

### 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
- Genearlizations 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

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

# 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
Leave a comment

## Reflection on the coloring and chromatic numbers

Joint work with Chris Lambie-Hanson. Abstract. We prove that reflection of the coloring number of a graph is consistent with non-reflection of the chromatic number. Moreover, it is proved that incompactness for the chromatic number of graphs (with arbitrarily large … Continue reading