### Archives

### Recent blog posts

- A strong form of König’s lemma October 21, 2017
- 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

### Keywords

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

# 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
11 Comments