A tale of hybrid mice
نویسنده
چکیده
We develop the basic theory of hod mice below ADR+“Θ is regular”. Woven into this theory is a proof of the Mouse Set Conjecture in the minimal model of ADR + “Θ is regular”. Once the basic theory is available, it can be applied to questions of evaluating consistency strengths of set theoretic hypothesis in terms of large cardinals. One such application is that the consistency of ADR + “Θ is regular” follows from the consistency of a Woodin limit of Woodins. Other applications use the core model induction but those are beyond the scope of this paper and will appear elsewhere (see [18], [19], [20] and [21]).
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