Solovay models and forcing extensions
Bagaria, Joan ; Bosch, Roger
J. Symbolic Logic, Tome 69 (2004) no. 1, p. 742-766 / Harvested from Project Euclid
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We study the preservation under projective ccc forcing extensions of the property of L(ℝ) being a Solovay model. We prove that this property is preserved by every strongly-Σ31 absolutely-ccc forcing extension, and that this is essentially the optimal preservation result, i.e., it does not hold for δ31 absolutely-ccc forcing notions. We extend these results to the higher projective classes of ccc posets, and to the class of all projective ccc posets, using definably-Mahlo cardinals. As a consequence we obtain an exact equiconsistency result for generic absoluteness under projective absolutely-ccc forcing notions.
Publié le : 2004-09-14
Classification:  Solovay models,  generic absoluteness,  definably-Mahlo cardinals,  productive-ccc partial orderings,  03E15,  03E35 
@article{1096901764,
     author = {Bagaria, Joan and Bosch, Roger},
     title = {Solovay models and forcing extensions},
     journal = {J. Symbolic Logic},
     volume = {69},
     number = {1},
     year = {2004},
     pages = { 742-766},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1096901764}
}

Bagaria, Joan; Bosch, Roger. Solovay models and forcing extensions. J. Symbolic Logic, Tome 69 (2004) no. 1, pp.  742-766. http://gdmltest.u-ga.fr/item/1096901764/