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A very discontinuous Borel function

Published online by Cambridge University Press:  12 March 2014

Juris Steprāns
Juris Steprāns*
Affiliation:
Department of Mathematics, York University, North York, Ontario, CanadaM3J IP3
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Abstract

It is shown to be consistent that the reals are covered by ℵ1, meagre sets yet there is a Baire class 1 function which cannot be covered by fewer than ℵ2, continuous functions. A new cardinal invariant is introduced which corresponds to the least number of continuous functions required to cover a given function. This is characterized combinatorially. A forcing notion similar to, but not equivalent to, superperfect forcing is introduced.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 58 , Issue 4 , December 1993 , pp. 1268 - 1283
Copyright
Copyright © Association for Symbolic Logic 1993

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References

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