### 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

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

# 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