منابع مشابه
Projective Forcing
We study the projective posets and their properties as forcing notions. We also define Martin’s axiom restricted to projective sets, MA(proj), and show that this axiom is weaker than full Martin’s axiom by proving the consistency of ZFC + XH + MA(proj) with “there exists a Suslin tree”, “there exists a non-strong gap”, “there exists an entangled set of reals” and “there exists K < 2No such that...
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 کاملProjective Absoluteness under Sacks Forcing
We show that Σ3-absoluteness under Sacks forcing is equivalent to the Sacks measurability of every ∆2 set of reals. We also show that Sacks forcing is the weakest forcing notion among all of the preorders which always add a new real with respect to Σ3 forcing absoluteness.
متن کاملForcing axioms and projective sets of reals
This paper is an introduction to forcing axioms and large cardinals. Specifically, we shall discuss the large cardinal strength of forcing axioms in the presence of regularity properties for projective sets of reals. The new result shown in this paper says that ZFC + the bounded proper forcing axiom (BPFA) + “every projective set of reals is Lebesgue measurable” is equiconsistent with ZFC + “th...
متن کاملSlow Forcing in the Projective Dynamics Method
We provide a proof that when there is no forcing the recently introduced projective dynamics Monte Carlo algorithm gives the exact lifetime of the metastable state, within statistical uncertainties. We also show numerical evidence illustrating that for slow forcing the approach to the zero-forcing limit is rather rapid. The model studied numerically is the 3-dimensional 3-state Potts ferromagnet.
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 1997
ISSN: 0168-0072
DOI: 10.1016/s0168-0072(96)00035-8