Core models in the presence of Woodin cardinals

2003/03/07 by Ralf Schindler, Schindler, Ralf
Mathematics · #03E35 #03E45 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topology and Set Theory #FOS: Mathematics #Logic (math.LO) #math.LO #msc:03E35 #msc:03E45

paper · pdf · doi:10.48550/arxiv.math/0303089

6 pages

arxiv created 2003/03/07 · openalex publication_date 2003/03/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is shown that if there is a measurable cardinal above n Woodin cardinals and M_n+1^# doesn't exist then K exists. K is not fully iterable, though, but only iterable with respect to stacks of certain trees living between the Woodin cardinals. However, it is still true that if M is an omega-closed iterate of V then K^M is an iterate of K.

Related

• Cardinal arithmetic and Woodin cardinals
• Mice with Woodin cardinals from a Reinhardt
• The covering lemma up to a Woodin cardinal
• Varsovian models II
• Strong Tree Properties for Small Cardinals