Title: The maximum principle in forcing and the axiom of choice
Author: Arnold W. Miller
Abstract:
In this paper we prove that the maximum principle in forcing
is equivalent to the axiom of choice.
The maximum principle is the property of forcing:
p ||- exists x theta(x) iff for some name tau p ||- theta(tau).
We also look at three similar partial orders in the Basic Cohen model
for the failure of the axiom of choice. We show that despite
their apparent similarity the maximum principle holds for only
one of the three.
LaTex2e: 14 pages
Latest version at: www.math.wisc.edu/~miller