Name: Arnold W. Miller
Title: The hierarchy of ω1-Borel sets

The family ω1-Borel sets is the smallest family of subsets of the real line
which contains the family of open sets and is closed under complementation
and ω1 unions. We show:
Theorem 1. MA+notCH implies this hierarchy has length ω2.
Theorem 2. In the Cohen real model it has length either ω1+1 or ω1+2.
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