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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

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

# 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
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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