On relatively analytic and Borel subsets
Miller, Arnold W.
J. Symbolic Logic, Tome 70 (2005) no. 1, p. 346-352 / Harvested from Project Euclid
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Define 𝖟 to be the smallest cardinality of a function f : X→ Y with X,Y ⊆ 2ω such that there is no Borel function g⊇ 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 ωω. This answers a question raised by Zapletal. ¶ We also show that it is relatively consistent with ZFC that there exists X⊆ 2ω 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.
Publié le : 2005-03-14
Classification:  03E35,  03E17,  03E15 
@article{1107298524,
     author = {Miller, Arnold W.},
     title = {On relatively analytic and Borel subsets},
     journal = {J. Symbolic Logic},
     volume = {70},
     number = {1},
     year = {2005},
     pages = { 346-352},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1107298524}
}

Miller, Arnold W. On relatively analytic and Borel subsets. J. Symbolic Logic, Tome 70 (2005) no. 1, pp.  346-352. http://gdmltest.u-ga.fr/item/1107298524/