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- Title
The reverse mathematics of non-decreasing subsequences.
- Authors
Patey, Ludovic
- 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.
- Subjects
REVERSE mathematics; RAMSEY numbers; MATHEMATICS theorems; ARITHMETIC; AXIOMS
- Publication
Archive for Mathematical Logic, 2017, Vol 56, Issue 5/6, p491
- ISSN
0933-5846
- Publication type
Article
- DOI
10.1007/s00153-017-0536-9