论文信息 - THE MOUSE SET CONJECTURE FOR SETS OF REALS

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. †

John Steel | Grigor Sargsyan | J. Steel | G. Sargsyan

[1] M. Foreman,et al. Handbook of Set Theory , 2010 .

[2] J. Steel. Derived models associated to mice , 2007 .

[3] Grigor Sargsyan,et al. A tale of hybrid mice , 2009 .

[4] John R. Steel. Scales in K(R) , 2008 .

[5] Ralf Schindler,et al. The core model induction , 2007 .

[6] Steve Jackson,et al. Structural Consequences of AD , 2010 .

[7] Ralf Schindler,et al. The self-iterability of L[E] , 2009, J. Symb. Log..

[9] G. Sargsyan. Covering with universally Baire operators , 2015 .

[10] John R. Steel,et al. An Outline of Inner Model Theory , 2010 .