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w1 and w1* may be the only minimal uncountable order types.
by
Justin Tatch Moore
Boise State University
Both w1 and w1* have the property that they embed into all of their uncountable suborders. Baumgartner asked if there are any other ZFC examples. PFA implies that there are five such examples and Baumgartner demonstrated that diamond+ implies that there is a Specker type which is minimal. I will show that it is consistent with CH that no minimal uncountable ordertypes other than w1 and w1* exist. This involves showing that a weak form of ladder system uniformization is consistent with CH but that, in the presence of a minimal Specker type, that this form of uniformization implies 2w = 2w1.
Date received: February 23, 2005
Copyright © 2005 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # capk-05.