On ordinal ranks of Baire class functions
Tom 247 / 2019
Fundamenta Mathematicae 247 (2019), 109-130
MSC: Primary 26A21; Secondary 03E15, 54H05.
DOI: 10.4064/fm616-3-2019
Opublikowany online: 5 September 2019
Streszczenie
The theory of ordinal ranks on Baire class 1 functions developed by Kechris and Loveau was extended by Elekes, Kiss and Vidnyánszky (2016) to Baire class functions for any countable ordinal \xi \geq 1. We answer two of the questions raised by them. Specifically, we show that for any countable ordinal \xi \geq 1, the ranks \beta _{\xi }^{\ast } and \gamma _{\xi }^{\ast } are essentially equivalent, and that neither of them is essentially multiplicative. Since the rank \beta is not essentially multiplicative, we investigate further its behavior with respect to products. We characterize the functions f such that \beta (fg)\leq \omega ^{\xi } whenever \beta (g)\leq \omega ^{\xi } for any countable ordinal \xi .
