Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 61, Number 2 (2020), 245-263.
An Effective Analysis of the Denjoy Rank
We analyze the descriptive complexity of several -ranks from classical analysis which are associated to Denjoy integration. We show that , , , and are -complete, answering a question of Walsh in case of . Furthermore, we identify the precise descriptive complexity of the set of functions obtainable with at most steps of the transfinite process of Denjoy totalization: if is the -rank naturally associated to , , or , and if , then is -complete. These finer results are an application of the author’s previous work on the limsup rank on well-founded trees. Finally, and are -complete, answering more questions of Walsh.
Notre Dame J. Formal Logic, Volume 61, Number 2 (2020), 245-263.
Received: 31 October 2017
Accepted: 4 November 2019
First available in Project Euclid: 4 April 2020
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 03E15: Descriptive set theory [See also 28A05, 54H05]
Secondary: 26A39: Denjoy and Perron integrals, other special integrals
Westrick, Linda. An Effective Analysis of the Denjoy Rank. Notre Dame J. Formal Logic 61 (2020), no. 2, 245--263. doi:10.1215/00294527-2020-0006. https://projecteuclid.org/euclid.ndjfl/1585965655