Archive for Mathematical Logic 48 (7):679-690 (2009)

Abstract
We show that ${{\bf \Sigma}^1_3}$ -absoluteness for Sacks forcing is equivalent to the non-existence of a ${{\bf \Delta}^1_2}$ Bernstein set. We also show that Sacks forcing is the weakest forcing notion among all of the preorders that add a new real with respect to ${{\bf \Sigma}^1_3}$ forcing absoluteness
Keywords Forcing absoluteness  Sacks forcing  Bernstein sets
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DOI 10.1007/s00153-009-0143-5
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References found in this work BETA

Set Theory.T. Jech - 2005 - Bulletin of Symbolic Logic 11 (2):243-245.
Δ12-Sets of Reals.Jaime I. Ihoda & Saharon Shelah - 1989 - Annals of Pure and Applied Logic 42 (3):207-223.
Solovay-Type Characterizations for Forcing-Algebras.Jörg Brendle & Benedikt Löwe - 1999 - Journal of Symbolic Logic 64 (3):1307-1323.
Amoeba-Absoluteness and Projective Measurability.Jörg Brendle - 1993 - Journal of Symbolic Logic 58 (4):1284-1290.

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Citations of this work BETA

Forcing Absoluteness and Regularity Properties.Daisuke Ikegami - 2010 - Annals of Pure and Applied Logic 161 (7):879-894.

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