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Paul
Posts:
676
Registered:
7/12/10


Problem understanding detail in Szemeredi's proof of theorem on arithmetic progressions.
Posted:
Feb 17, 2014 5:28 PM


Szemeredi's proof that subsets of the natural numbers which have positive upper density contain arbitrarily long arithmetical progressions is available here:
http://matwbn.icm.edu.pl/ksiazki/aa/aa27/aa27132.pdf
I am stuck on Fact 6 (page 212) because I don't follow the "induction" argument that X' and R have nonempty intersection.
There is no need to point out that simpler expositions of the proof (for example Tao's) are available. I'm aware of this but would like to read the original historical proof.
Many thanks for your help. Paul Epstein



