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### 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

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

# 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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