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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.
    We study the projective posets and their properties as forcing notions. We also define Martin's axiom restricted to projective sets, MA, and show that this axiom is weaker than full Martin's axiom by proving the consistency of ZFC + ¬lCH + MA with “there exists a Suslin tree”, “there exists a non-strong gap”, “there exists an entangled set of reals” and “there exists κ < 20 such that 20 < 2k”.
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