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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

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

# 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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