Name: Arnold W. Miller

Title: The hierarchy of ω

Abstract:

The family ω_{1}-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 ω_{1}
unions. We show:

Theorem 1. MA+notCH implies this hierarchy has length
ω_{2}.

Theorem 2. In the Cohen real model it has length either
ω_{1}+1 or ω_{1}+2.

LaTex2e: 12 pages

Latest version at: www.math.wisc.edu/~miller