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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

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

# 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