Filter descriptive classes of Borel functions

Gabriel Debs, and Jean Saint Raymond. "Filter descriptive classes of Borel functions." Fundamenta Mathematicae 204.3 (2009): 189-213. <http://eudml.org/doc/282655>.

@article{GabrielDebs2009,
abstract = {We first prove that given any analytic filter ℱ on ω the set of all functions f on $2^\{ω\}$ which can be represented as the pointwise limit relative to ℱ of some sequence $(fₙ)_\{n∈ω\}$ of continuous functions ($f = lim_\{ℱ\} fₙ$), 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.},
author = {Gabriel Debs, Jean Saint Raymond},
journal = {Fundamenta Mathematicae},
keywords = {analytic filters; Borel functions},
language = {eng},
number = {3},
pages = {189-213},
title = {Filter descriptive classes of Borel functions},
url = {http://eudml.org/doc/282655},
volume = {204},
year = {2009},
}

TY - JOUR
AU - Gabriel Debs
AU - Jean Saint Raymond
TI - Filter descriptive classes of Borel functions
JO - Fundamenta Mathematicae
PY - 2009
VL - 204
IS - 3
SP - 189
EP - 213
AB - We first prove that given any analytic filter ℱ on ω the set of all functions f on $2^{ω}$ which can be represented as the pointwise limit relative to ℱ of some sequence $(fₙ)_{n∈ω}$ of continuous functions ($f = lim_{ℱ} fₙ$), 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.
LA - eng
KW - analytic filters; Borel functions
UR - http://eudml.org/doc/282655
ER -