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Proper forcing and L(ℝ)

Published online by Cambridge University Press:  12 March 2014

Itay Neeman  and
Jindřich Zapletal
Itay Neeman*
Affiliation:
Harvard University, Department of Mathematics, One Oxford St., Cambridge, MA 02138, USA
Jindřich Zapletal*
Affiliation:
Department of Mathematics, Dartmouth College, Hanover, NH 03755, USA
*
Department of Mathematics, University of California, Los Angeles, CA, 90095-1555, USA, E-mail: ineeman@math.ucla.edu
Department of Mathematics, University of Florida, Gainsville, FL 32611-8105, USA, E-mail: zapletal@math.ufl.edu
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Abstract

We present two ways in which the model L(ℝ) is canonical assuming the existence of large cardinals. We show that the theory of this model, with ordinal parameters, cannot be changed by small forcing: we show further that a set of ordinals in V cannot be added to L(ℝ) by small forcing. The large cardinal needed corresponds to the consistency strength of ADL(ℝ): roughly ω Woodin cardinals.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 66 , Issue 2 , June 2001 , pp. 801 - 810
Copyright
Copyright © Association for Symbolic Logic 2001

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References

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