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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

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

# 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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