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  1. Joan Bagaria & Roger Bosch (2004). Proper Forcing Extensions and Solovay Models. Archive for Mathematical Logic 43 (6):739-750.
    We study the preservation of the property of being a Solovay model under proper projective forcing extensions. We show that every strongly-proper forcing notion preserves this property. This yields that the consistency strength of the absoluteness of under strongly-proper forcing notions is that of the existence of an inaccessible cardinal. Further, the absoluteness of under projective strongly-proper forcing notions is consistent relative to the existence of a -Mahlo cardinal. We also show that the consistency strength of the absoluteness of under (...)
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  2. Joan Bagaria & Roger Bosch (2004). Solovay Models and Forcing Extensions. Journal of Symbolic Logic 69 (3):742-766.
    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 Σ₃¹ 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 (...)
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  3. Eva Álvarez, Roger Bosch & Lorena Villamil (eds.) (2003). Volume of Abstracts: 12th International Congress of Logic, Methodology, and Philosophy of Science, Oviedo, August 7-13, 2003. [REVIEW] Departamento de Filosofía, Universidad de Oviedo.
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  4. Roger Bosch (2003). Demostrar Teoremas Con Forcing. Teorema 22 (3):17-36.
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  5. Joan Bagaria & Roger Bosch (1997). Projective Forcing. Annals of Pure and Applied Logic 86 (3):237-266.
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