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Archive for Mathematical Logic

, Volume 56, Issue 5–6, pp 491–506 | Cite as

The reverse mathematics of non-decreasing subsequences

  • Ludovic PateyEmail author
Article
  • 53 Downloads

Abstract

Every function over the natural numbers has an infinite subdomain on which the function is non-decreasing. Motivated by a question of Dzhafarov and Schweber, we study the reverse mathematics of variants of this statement. It turns out that this statement restricted to computably bounded functions is computationally weak and does not imply the existence of the halting set. On the other hand, we prove that it is not a consequence of Ramsey’s theorem for pairs. This statement can therefore be seen as an arguably natural principle between the arithmetic comprehension axiom and stable Ramsey’s theorem for pairs.

Keywords

Reverse mathematics Non-decreasing subsequence Ramsey’s theorem 

Mathematics Subject Classification

03B30 03F35 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Dept. of MathematicsUniversity of California, BerkeleyBerkeleyUSA

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