Proper forcings and absoluteness in L ( ℝ )

Itay Neeman; Jindřich Zapletal

Commentationes Mathematicae Universitatis Carolinae (1998)

  • Volume: 39, Issue: 2, page 281-301
  • ISSN: 0010-2628

Abstract

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We show that in the presence of large cardinals proper forcings do not change the theory of L ( ℝ ) with real and ordinal parameters and do not code any set of ordinals into the reals unless that set has already been so coded in the ground model.

How to cite

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Neeman, Itay, and Zapletal, Jindřich. "Proper forcings and absoluteness in $L(\mathbb {R})$." Commentationes Mathematicae Universitatis Carolinae 39.2 (1998): 281-301. <http://eudml.org/doc/248282>.

@article{Neeman1998,
abstract = {We show that in the presence of large cardinals proper forcings do not change the theory of $L(\mathbb \{R\})$ with real and ordinal parameters and do not code any set of ordinals into the reals unless that set has already been so coded in the ground model.},
author = {Neeman, Itay, Zapletal, Jindřich},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {proper forcing; large cardinals; proper forcing; large cardinals},
language = {eng},
number = {2},
pages = {281-301},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Proper forcings and absoluteness in $L(\mathbb \{R\})$},
url = {http://eudml.org/doc/248282},
volume = {39},
year = {1998},
}

TY - JOUR
AU - Neeman, Itay
AU - Zapletal, Jindřich
TI - Proper forcings and absoluteness in $L(\mathbb {R})$
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1998
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 39
IS - 2
SP - 281
EP - 301
AB - We show that in the presence of large cardinals proper forcings do not change the theory of $L(\mathbb {R})$ with real and ordinal parameters and do not code any set of ordinals into the reals unless that set has already been so coded in the ground model.
LA - eng
KW - proper forcing; large cardinals; proper forcing; large cardinals
UR - http://eudml.org/doc/248282
ER -

References

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  9. Neeman I., Zapletal J., Proper forcing and L ( ℝ ) , J. London Math. Soc. submitted. 
  10. Schimmerling E., handwritten notes of W.H. Woodin's lectures, . 
  11. Shelah S., Proper Forcing, Springer Verlag Berlin (1981), Lecture Notes in Math. 940. (1981) MR0675955
  12. Woodin W.H., Supercompact cardinals, sets of reals and weakly homogeneous trees, Proc. Natl. Acad. Sci. USA 85 (1988), 6587-6591. (1988) Zbl0656.03037MR0959110
  13. Woodin W.H., The axiom of determinacy, forcing axioms and the nonstationary ideal, to appear. Zbl0954.03046MR1713438

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