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THE MOUSE SET CONJECTURE FOR SETS OF REALS

Published online by Cambridge University Press:  22 April 2015

GRIGOR SARGSYAN  and
JOHN STEEL
GRIGOR SARGSYAN
Affiliation:
DEPARTMENT OF MATHEMATICS RUTGERS UNIVERSITY 110 FRELINGHUYSEN RD PISCATAWAY, NJ 08854, USAURL: http://math.rutgers.edu/∼gs481E-mail: [email protected]
JOHN STEEL
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF CALIFORNIA BERKELEY, CALIFORNIA 94720, USAURL: http://math.berkeley.edu/∼steelE-mail: [email protected]
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Abstract

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.

Keywords

03E1503E4503E60Mouseinner model theorydescriptive set theoryhod mouse
Type
Articles
Information
The Journal of Symbolic Logic , Volume 80 , Issue 2 , June 2015 , pp. 671 - 683
Copyright
Copyright © The Association for Symbolic Logic 2015 

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References

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