Journal of Symbolic Logic 70 (1):346 - 352 (2005)

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
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DOI 10.2178/jsl/1107298524
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References found in this work BETA

On the Length of Borel Hierarchies.Arnorld W. Miller - 1979 - Annals of Mathematical Logic 16 (3):233.

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Forcing with Quotients.Michael Hrušák & Jindřich Zapletal - 2008 - Archive for Mathematical Logic 47 (7-8):719-739.

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