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ON THE STRENGTH OF TWO RECURRENCE THEOREMS

Published online by Cambridge University Press:  29 September 2016

ADAM R. DAY
ADAM R. DAY*
Affiliation:
SCHOOL OF MATHEMATICS, STATISTICS AND OPERATIONS RESEARCH VICTORIA UNIVERSITY OF WELLINGTON WELLINGTON, NEW ZEALAND E-mail: [email protected]
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Abstract

This paper uses the framework of reverse mathematics to investigate the strength of two recurrence theorems of topological dynamics. It establishes that one of these theorems, the existence of an almost periodic point, lies strictly between WKL and ACA (working over RCA0). This is the first example of a theorem with this property. It also shows the existence of an almost periodic point is conservative over RCA0 for ${\rm{\Pi }}_1^1$ -sentences.

Keywords

Reverse mathematicsdynamical systemsrecurrencecomputability theory
Type
Articles
Information
The Journal of Symbolic Logic , Volume 81 , Issue 4 , December 2016 , pp. 1357 - 1374
Copyright
Copyright © The Association for Symbolic Logic 2016 

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References

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