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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

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

# Tag Archives: incompactness

## 2017 Workshop in Set Theory, Oberwolfach

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

## Chromatic numbers of graphs – large gaps

Abstract. We say that a graph $G$ is $(\aleph_0,\kappa)$-chromatic if $\text{Chr}(G)=\kappa$, while $\text{Chr}(G’)\le\aleph_0$ for any subgraph $G’$ of $G$ of size $<|G|$. The main result of this paper reads as follows. If $\square_\lambda+\text{CH}_\lambda$ holds for a given uncountable cardinal $\lambda$, … Continue reading

Posted in Compactness, Infinite Graphs, Publications
Tagged 03E35, 05C15, 05C63, Almost countably chromatic, Chromatic number, incompactness, Ostaszewski square
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