Mathematics – Logic
Scientific paper
2011-07-25
Mathematics
Logic
LaTex2e: 12 pages Latest version at: http://www.math.wisc.edu/~miller
Scientific paper
The family omega1-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 omega1 unions. We show:
Theorem 1. MA+notCH implies this hierarchy has length omega2.
Theorem 2. In the Cohen real model it has length either omega1+1 or omega1+2.
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