### Archives

### Recent blog posts

- A strong form of König’s lemma October 21, 2017
- 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

### Keywords

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

# 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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