Journal of Symbolic Logic

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

Itay Neeman and Jindrich Zapletal

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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.

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

First available in Project Euclid: 6 July 2007

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Neeman, Itay; Zapletal, Jindrich. Proper Forcing and L$(\mathbb{R})$. J. Symbolic Logic 66 (2001), no. 2, 801--810.

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