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Iterating ordinal definability

By Wlodzimierz Zadrozny


AbstractThe paper presents a uniform way of obtaining by forcing descending sequences of the iterations of HOD and describes their structure. Among other things the following results are proved:Theorem. Any model M of ZFC can be obtained by the transfinite iteration of HOD in some generic extension N of M, i.e. M=(HODOn)N.Theorem (ZFC). For any ordinal α there is a complete Boolean algebra B with a decreasing sequence of derivatives of length α.Moreover some other results about ordinal definability are reproved using the introduced method. This method is a refinement of the classical method of coding introduced by McAloon in [11]

Publisher: Published by Elsevier B.V.
Year: 1983
DOI identifier: 10.1016/0168-0072(83)90008-8
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