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- 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

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

# 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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