We first prove that given any analytic filter ℱ on ω the set of all functions f on which can be represented as the pointwise limit relative to ℱ of some sequence of continuous functions (), is exactly the set of all Borel functions of class ξ for some countable ordinal ξ that we call the rank of ℱ. We discuss several structural properties of this rank. For example, we prove that any free Π⁰₄ filter is of rank 1.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm204-3-1,
author = {Gabriel Debs and Jean Saint Raymond},
title = {Filter descriptive classes of Borel functions},
journal = {Fundamenta Mathematicae},
volume = {205},
year = {2009},
pages = {189-213},
zbl = {1179.03046},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm204-3-1}
}
Gabriel Debs; Jean Saint Raymond. Filter descriptive classes of Borel functions. Fundamenta Mathematicae, Tome 205 (2009) pp. 189-213. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm204-3-1/