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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

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

# 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