### 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

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

# 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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