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In this last part we briefly review what is known of core models beyond K. Much, it turns out, is known about models and mice and very little about covering lemmas and SCH.
In the final chapter we discuss the present state of knowledge about SCH. It was once thought that large cardinal axioms might settle the GCH. This has turned out not to be the case: powers of regular cardinals do as they please, irrespective of large cardinals. On the other hand it looks possible that large cardinals might partially settle SCH (partially because we only get relative consistency results from the cardinals). The division of large cardinals into two camps may mark a fundamental change in the nature of cardinality axioms; or it may say no more than that Prikry sequences and fine structure do not go together.
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