Iterated forcing and normal ideals onω
1 |
| |
Authors: | Saharon Shelah |
| |
Institution: | (1) Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel;(2) Department of Mathematics and EECS, University of Michigan, Ann Arbor, Michigan, USA;(3) Department of Mathematics, Rutgers University, New Brunswick, New Jersey, USA |
| |
Abstract: | We prove that suitable iteration does not collapse ℵ1 and does not add reals], i.e., that in such iteration, certain sealing of maximal antichains of stationary subsets ofω
1 is allowed. As an application, e.g., we prove from supercompact hypotheses, mainly, the consistency of: ZFC + GCH + “for
some stationary setS ⊆ω
1, {ie345-1}(ω
1)/(D
ω
1 +S) is the Levy algebra” (i.e., the complete Boolean Algebra corresponding to the Levy collapse Levy (ℵ0,<ℵ2) (and we can add “a variant of PFA”) and the consistency of the same, with “Ulam property” replacing “Levy algebra”). The
paper assumes no specialized knowledge (if you agree to believe in the semi-properness iteration theorem and RCS iteration).
This research was partially supported by the NSF.
This paper was largely written during the author’s visit at Cal Tech around the end of April 1985. The author would like to
thank M. Foreman, A. Kekris and H. Woodin for their hospitality. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|