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THE MOUSE SET CONJECTURE FOR SETS OF REALS

  • GRIGOR SARGSYAN (a1) and JOHN STEEL (a2)

Abstract

We show that the Mouse Set Conjecture for sets of reals is true in the minimal model of AD + “Θ is regular”. As a consequence, we get that below AD + “Θ is regular”, models of AD+AD are hybrid mice over ℝ. Such a representation of models of AD+ is important in core model induction applications.

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[1]Jackson, Steve, Structural consequences of AD, Handbook of set theory. pp. 17531876, Springer, Dordrecht, 2010.
[2]Sargsyan, Grigor, A tale of hybrid mice, ProQuest LLC, Ann Arbor, MI, 2009. Ph.D. Thesis, University of California, Berkeley.
[3]Sargsyan, Grigor, A tale of hybrid mice, Memoirs of American Mathematical Society, to appear, available athttp://math.rutgers.edu/∼gs481/, 2013.
[4]Sargsyan, Grigor, Covering with universally Baire operators, available at http://math.rutgers.edu/∼gs481/.
[5]Sargsyan, Grigor and Trang, Nam, Non-tame mouse from tame failures of the unique branch hypothesis, available at http://math.rutgers.edu/∼gs481/.
[6]Schindler, Ralf and Steel, John, The self-iterability of L[E], this Journal, vol. 74 (2009), no. 3, pp. 751779.
[7]Schindler, Ralf and Steel, John, The core model induction, available at math.berkeley.edu/∼steel.
[8]Steel, John R., Scales in K(ℝ). The cabal seminar, vol. 1 (2003), pp. 176208.
[9]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. 105193, World Scientific Publisher, Hackensack, NJ, 2008.
[10]Steel, John R., An optimal consistency strength lower bound for AD , unpublished notes, 2008.
[11]Steel, John R., An outline of inner model theory, Handbook of set theory. Vols. 1, 2, 3, pp. 15951684, Springer, Dordrecht, 2010.

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THE MOUSE SET CONJECTURE FOR SETS OF REALS

  • GRIGOR SARGSYAN (a1) and JOHN STEEL (a2)

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