منابع مشابه
Generic absoluteness
We explore the consistency strength of 1 3 and 1 4 absoluteness, for a variety of forcing notions.
متن کاملAxioms of Generic Absoluteness
We give a unified presentation of the set-theoretic 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 set-theoretic axioms, and we provide a list of the main open problems.
متن کاملGeneric 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 Axiom holds for Σ ∼ 1 n partial orderings, but it fails for the Σ ∼ 1 n+1.
متن کاملGeneric Σ 1 3 Absoluteness
In this article we study the strength of Σ 1 3 absoluteness (with real parameters) in various types of generic extensions, correcting and improving some results from [2]. We shall also make some comments relating this work to the bounded forcing axioms BMM, BPFA and BSPFA. The statement " Σ 1 3 absoluteness holds for ccc forcing " means that if a Σ 1 3 formula with real parameters has a solutio...
متن کاملGeneric Absoluteness and the Continuum
Let Hω2 denote the collection of all sets whose transitive closure has size at most א1. Thus, (Hω2 ,∈) is a natural model of ZFC minus the power-set axiom which correctly estimates many of the problems left open by the smaller and better understood structure (Hω1 ,∈) of hereditarily countable sets. One of such problems is, for example, the Continuum Hypothesis. It is largely for this reason tha...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2001
ISSN: 0168-0072
DOI: 10.1016/s0168-0072(00)00038-5