Periodic points and subsystems of second-order arithmetic

Annals of Pure and Applied Logic 62 (1):51-64 (1993)

Abstract

We study the formalization within sybsystems of second-order arithmetic of theorems concerning periodic points in dynamical systems on the real line. We show that Sharkovsky's theorem is provable in WKL0. We show that, with an additional assumption, Sharkovsky's theorem is provable in RCA0. We show that the existence for all n of n-fold iterates of continuous mappings of the closed unit interval into itself is equivalent to the disjunction of Σ02 induction and weak König's lemma

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Citations of this work

Splittings and Disjunctions in Reverse Mathematics.Sam Sanders - 2020 - Notre Dame Journal of Formal Logic 61 (1):51-74.
Fundamental Notions of Analysis in Subsystems of Second-Order Arithmetic.Jeremy Avigad - 2006 - Annals of Pure and Applied Logic 139 (1):138-184.
WKL 0 and Induction Principles in Model Theory.David R. Belanger - 2015 - Annals of Pure and Applied Logic 166 (7-8):767-799.
On the Strength of Two Recurrence Theorems.Adam R. Day - 2016 - Journal of Symbolic Logic 81 (4):1357-1374.

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