Proper Forcing and L$(\mathbb{R})$
Neeman, Itay ; Zapletal, Jindrich
J. Symbolic Logic, Tome 66 (2001) no. 1, p. 801-810 / Harvested from Project Euclid
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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.
Publié le : 2001-06-14
Classification:  
@article{1183746474,
     author = {Neeman, Itay and Zapletal, Jindrich},
     title = {Proper Forcing and L$(\mathbb{R})$},
     journal = {J. Symbolic Logic},
     volume = {66},
     number = {1},
     year = {2001},
     pages = { 801-810},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183746474}
}

Neeman, Itay; Zapletal, Jindrich. Proper Forcing and L$(\mathbb{R})$. J. Symbolic Logic, Tome 66 (2001) no. 1, pp.  801-810. http://gdmltest.u-ga.fr/item/1183746474/