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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

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

# Tag Archives: reflection principles

## The reflection principle $R_2$

A few years ago, in this paper, I introduced the following reflection principle: Definition. $R_2(\theta,\kappa)$ asserts that for every function $f:E^\theta_{<\kappa}\rightarrow\kappa$, there exists some $j<\kappa$ for which the following set is nonstationary: $$A_j:=\{\delta\in E^\theta_\kappa\mid f^{-1}[j]\cap\delta\text{ is nonstationary}\}.$$ I wrote there … Continue reading

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Tagged reflection principles, square, stationary reflection, Weakly compact cardinal
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## 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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