### 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

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

# 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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