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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
- Genearlizations 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

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

# 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 a graph is consistent with non-reflection of the chromatic number. Moreover, it is proved that incompactness for the chromatic number of graphs (with arbitrarily large … 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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