On relatively analytic and Borel subsets

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

Define z to be the smallest cardinality of a function f:X->Y with X and Y sets of reals such that there is no Borel function g extending f. In this paper we prove that it is relatively consistent with ZFC to have b<z where b is, as usual, smallest cardinality of an unbounded family in w^w. This answers a question raised by Zapletal. We also show that it is relatively consistent with ZFC that there exists a set of reals X such that the Borel order of X is bounded but there exists a relatively analytic subset of X which is not relatively coanalytic. This answers a question of Mauldin.
LaTeX2e 10 pages available at http://www.math.wisc.edu/~miller/res/index.html

Keywords

Logic, 03E35; 03E17; 03E15

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/67348

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0305036
 http://arxiv.org/abs/math/0305036

Collections

arXiv