### 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

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

# 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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