### Archives

### Recent blog posts

- A strong form of König’s lemma October 21, 2017
- 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

### Keywords

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

# Tag Archives: coloring number

## 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
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 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