The mouse Set conjecture for Sets of Reals
We show that the Mouse Set Conjecture for sets of reals is true in the minimal model of ADR + “Θ is regular”. As a consequence, we get that below ADR + “Θ is regular”, models of AD + +¬ADR are hybrid mice over R. Such a representation of models of AD+ is important in core model induction applications. One of the central open problems in descriptive inner model theory is the conjecture known as the Mouse Set Conjecture (MSC). It conjectures that under AD ∗2000 Mathematics Subject Classifications: 03E15, 03E45, 03E60. †