### Archives

### 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

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

# Tag Archives: Rado’s conjecture

## 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

## Square principles

Since the birth of Jensen’s original Square principle, many variations of the principle were introduced and intensively studied. Asaf Karagila suggested me today to put some order into all of these principles. Here is a trial. Definition. A square principle … Continue reading

## The chromatic numbers of the Erdos-Hajnal graphs

Recall that a coloring $c:G\rightarrow\kappa$ of an (undirected) graph $(G,E)$ is said to be chromatic if $c(v_1)\neq c(v_2)$ whenever $\{v_1,v_2\}\in E$. Then, the chromatic number of a graph $(G,E)$ is the least cardinal $\kappa$ for which there exists a chromatic … Continue reading

Posted in Blog, Expository
Tagged Chromatic number, Erdos-Hajnal graphs, Rado's conjecture, reflection principles
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