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On relatively analytic and Borel subsets

Published online by Cambridge University Press:  12 March 2014

Arnold W. Miller
Arnold W. Miller*
Affiliation:
University of Wisconsin-Madison, Department of Mathematics, van Vleck Hall, 480 Lincoln Drive, Madison, Wisconsin 53706-1388, USA, E-mail: miller@math.wisc.edu, URL: http://www.math.wisc.edu/~miller
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Abstract

Define to be the smallest cardinality of a function f: X→Y with I, 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 < 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 Borei 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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 70 , Issue 1 , March 2005 , pp. 346 - 352
Copyright
Copyright © Association for Symbolic Logic 2005

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References

REFERENCES

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