Abstract:
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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