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March 2005 On relatively analytic and Borel subsets
Arnold W. Miller
J. Symbolic Logic 70(1): 346-352 (March 2005). DOI: 10.2178/jsl/1107298524

Abstract

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.

Citation

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Arnold W. Miller. "On relatively analytic and Borel subsets." J. Symbolic Logic 70 (1) 346 - 352, March 2005. https://doi.org/10.2178/jsl/1107298524

Information

Published: March 2005
First available in Project Euclid: 1 February 2005

zbMATH: 1083.03045
MathSciNet: MR2119137
Digital Object Identifier: 10.2178/jsl/1107298524

Subjects:
Primary: 03E15 , 03E17 , 03E35

Rights: Copyright © 2005 Association for Symbolic Logic

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Vol.70 • No. 1 • March 2005
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