Journal of Symbolic Logic

Proper Forcing and L$(\mathbb{R})$

Itay Neeman and Jindrich Zapletal

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Abstract

We present two ways in which the model L($\mathbb{R}$) 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($\mathbb{R}$) by small forcing. The large cardinal needed corresponds to the consistency strength of AD$^L(\mathbb{R})$; roughly $\omega$ Woodin cardinals.

Article information

Source
J. Symbolic Logic, Volume 66, Issue 2 (2001), 801-810.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183746474

Mathematical Reviews number (MathSciNet)
MR1833479

Zentralblatt MATH identifier
0988.03079

JSTOR
links.jstor.org

Citation

Neeman, Itay; Zapletal, Jindrich. Proper Forcing and L$(\mathbb{R})$. J. Symbolic Logic 66 (2001), no. 2, 801--810. https://projecteuclid.org/euclid.jsl/1183746474


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