### 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
- 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

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

## 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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