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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

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

# Tag Archives: incompactness

## 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

## 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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