Corpus ID: 118065677

Formulating Szemerédi's Theorem in Terms of Ultrafilters

  title={Formulating Szemer{\'e}di's Theorem in Terms of Ultrafilters},
  author={Heinrich-Gregor Zirnstein},
  journal={arXiv: Functional Analysis},
  • Heinrich-Gregor Zirnstein
  • Published 2012
  • Mathematics
  • arXiv: Functional Analysis
  • Van der Waerden's theorem asserts that if you color the natural numbers with, say, five different colors, then you can always find arbitrarily long sequences of numbers that have the same color and that form an arithmetic progression. Szemer\'edi's theorem generalizes this statement and asserts that every subset of natural numbers with positive density contains arithmetic progressions of arbitrary length. Van der Waerden's theorem can be proven using elementary combinatorics, but it is also… CONTINUE READING
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