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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

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

# 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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