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A covering theorem for the core model below a Woodin cardinal
The main result of this dissertation is a covering theorem for the core model below a Woodin cardinal. More precisely, we work with Steel's core model \K constructed in where is measurable. The theorem is in a similar spirit to theorems of Mitchell and Cox and roughly says that either \K recognizes the singularity of an ordinal or else is measurable in \K.The first chapter of the thesis builds up the technical theory we will work in. The premice we work with use Mitchell-Steel indexing, but we use Jensen's fine structure and a different amenable coding. The use of fine structure and this amenable coding significantly simplifies the theory. Towards the end of the first chapter, we prove the full condensation lemma for premice with Mitchell-Steel indexing. This was originally proven by Jensen for premice with -indexing. The second chapter is devoted to the proof of the above mentioned covering theorem
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