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### 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

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

# 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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