Hostname: page-component-76c49bb84f-lvxqv Total loading time: 0 Render date: 2025-07-13T15:06:32.884Z Has data issue: false hasContentIssue false
  • English
  • Français

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: grigor@math.rutgers.edu
JOHN STEEL
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF CALIFORNIA BERKELEY, CALIFORNIA 94720, USAURL: http://math.berkeley.edu/∼steelE-mail: steel@math.berkeley.edu
Get access Rights & Permissions [Opens in a new window]

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

Information

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

Jackson, Steve, Structural consequences of AD, Handbook of set theory. pp. 1753–1876, Springer, Dordrecht, 2010.Google Scholar
Sargsyan, Grigor, A tale of hybrid mice, ProQuest LLC, Ann Arbor, MI, 2009. Ph.D. Thesis, University of California, Berkeley.Google Scholar
Sargsyan, Grigor, A tale of hybrid mice, Memoirs of American Mathematical Society, to appear, available athttp://math.rutgers.edu/∼gs481/, 2013.Google Scholar
Sargsyan, Grigor, Covering with universally Baire operators, available at http://math.rutgers.edu/∼gs481/.Google Scholar
Sargsyan, Grigor and Trang, Nam, Non-tame mouse from tame failures of the unique branch hypothesis, available at http://math.rutgers.edu/∼gs481/.Google Scholar
Schindler, Ralf and Steel, John, The self-iterability of L[E], this Journal, vol. 74 (2009), no. 3, pp. 751–779.Google Scholar
Schindler, Ralf and Steel, John, The core model induction, available at math.berkeley.edu/∼steel.Google Scholar
Steel, John R., Scales in K(ℝ). The cabal seminar, vol. 1 (2003), pp. 176–208.Google Scholar
Steel, John R., Derived models associated to mice, Computational prospects of infinity. Part I, Tutorials, Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore, vol. 14, pp. 105–193, World Scientific Publisher, Hackensack, NJ, 2008.CrossRefGoogle Scholar
Steel, John R., An optimal consistency strength lower bound for AD ℝ, unpublished notes, 2008.Google Scholar
Steel, John R., An outline of inner model theory, Handbook of set theory. Vols. 1, 2, 3, pp. 1595–1684, Springer, Dordrecht, 2010.Google Scholar