Filter descriptive classes of Borel functions

• Autorzy: Gabriel Debs , Jean Saint Raymond
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
• 54A20: Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)
• 03E15: Descriptive set theory
• 03E45: Inner models, including constructibility, ordinal definability, and core models

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2009
• Tom: 204
• Numer: 3
• Strony: 189-213

Daty

wydano

2009

Twórcy

autor

Gabriel Debs

• Analyse Fonctionnelle, Institut de Mathématique de Jussieu, Boîte 186, 4, place Jussieu, 75252 Paris Cedex 05, France

autor

Jean Saint Raymond

• Analyse Fonctionnelle, Institut de Mathématique de Jussieu, Boîte 186, 4 place Jussieu, F- 75252 Paris Cedex 05, France

Identyfikatory

DOI

10.4064/fm204-3-1