### 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

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

# 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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