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AXIOMS OF GENERIC ABSOLUTENESS
"... Abstract. We give a unified presentation of the settheoretic axioms of generic absoluteness, we survey the known results regarding their consistency strength and some of their consequences as well as their relationship to other kinds of settheoretic axioms, and we provide a list of the main open p ..."
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Abstract. We give a unified presentation of the settheoretic axioms of generic absoluteness, we survey the known results regarding their consistency strength and some of their consequences as well as their relationship to other kinds of settheoretic axioms, and we provide a list of the main open problems. 1.
Generic absoluteness under projective forcing
"... We study the preservation of the property of L(R) being a Solovay model under projective ccc forcing extensions. We compute the exact consistency strength of the generic absoluteness of L(R) under forcing with projective ccc partial orderings and, as an application, we build models in which Martin’s ..."
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We study the preservation of the property of L(R) being a Solovay model under projective ccc forcing extensions. We compute the exact consistency strength of the generic absoluteness of L(R) under forcing with projective ccc partial orderings and, as an application, we build models in which Martin’s Axiom holds for Σ 1 n partial orderings, but it fails for the