### Archives

### 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

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

# 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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