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### 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

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Almost countably chromatic Fodor-type reflection Hindman's Theorem Stevo Todorcevic xbox Souslin Tree Successor of Regular Cardinal polarized partition relation ccc Distributive tree Rainbow sets Diamond Chang's conjecture Antichain 11P99 Fat stationary set Selective Ultrafilter Prevalent singular cardinals square principles coloring number Rock n' Roll Non-saturation stationary hitting Weakly compact cardinal stationary reflection b-scale diamond star Singular Density Uniformization Constructible Universe Mandelbrot set Partition Relations incompactness Absoluteness Small forcing Commutative cancellative semigroups Foundations Forcing Axioms Sakurai's Bell inequality Whitehead Problem Successor of Singular Cardinal Kurepa Hypothesis middle diamond reflection principles Singular cardinals combinatorics 05A17 HOD Generalized Clubs Slim tree Prikry-type forcing Ostaszewski square Hedetniemi's conjecture Uniformly coherent weak square Postprocessing function free Boolean algebra Martin's Axiom weak diamond Almost Souslin Axiom R Shelah's Strong Hypothesis Parameterized proxy principle Jonsson cardinal Knaster Hereditarily Lindelöf space Large Cardinals PFA Rado's conjecture Coherent tree square Cohen real Club Guessing Dushnik-Miller Universal Sequences Aronszajn tree Chromatic number Microscopic Approach sap Forcing OCA Erdos-Hajnal graphs Cardinal Invariants Erdos Cardinal tensor product graph Almost-disjoint famiy L-space projective Boolean algebra P-Ideal Dichotomy Ascent Path Fast club Square-Brackets Partition Relations Singular coﬁnality Cardinal function Nonspecial tree S-Space 05D10 approachability ideal very good scale Poset PFA(S)[S] Reduced Power Minimal Walks 20M14

# Tag Archives: Rainbow sets

## Prolific Souslin trees

In a paper from 1971, Erdos and Hajnal asked whether (assuming CH) every coloring witnessing $\aleph_1\nrightarrow[\aleph_1]^2_3$ has a rainbow triangle. The negative solution was given in a 1975 paper by Shelah, and the proof and relevant definitions may be found … Continue reading

Posted in Blog, Expository
Tagged Rainbow sets, Souslin Tree, Square-Brackets Partition Relations
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## Polychromatic colorings

These are lectures notes of two talks Dani Livne gave in our Infinite Combinatorics seminar. I did not take notes in real-time, hence, all possible mistakes here are due to myself. Recall that a function $f:A\rightarrow B$ is said to … Continue reading

## Comparing rectangles with squares through rainbow sets

In Todorcevic’s class last week, he proved all the results of Chapter 8 from his Walks on Ordinals book, up to (and including) Theorem 8.1.11. The upshots are as follows: Every regular infinite cardinal $\theta$ admits a naturally defined function … Continue reading