@article{5ae09af84443429e818c1a5568927dd4,
title = "Projective absoluteness for Sacks forcing",
abstract = "We show that ∑1/3-absoluteness for Sacks forcing is equivalent to the non-existence δ1/2 of a 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 ∑1/3 forcing absoluteness.",
keywords = "Bernstein sets, Forcing absoluteness, Sacks forcing",
author = "Daisuke Ikegami",
note = "Funding Information: The author would like to thank Joan Bagaria, through whose lecture in Kobe he became interested in forcing absoluteness. He also appreciates the help given by Yasuo Yoshinobu, who gave him useful comments on this paper and made the proof of Theorem 3.1 very simple. He is grateful to J{\"o}rg Brendle for helpful comments on Remark 3.2. Finally, he thanks the referee for several comments on this paper. This research was supported by a GLoRiClass fellowship funded by the European Commission (Early Stage Research Training Mono-Host Fellowship MEST-CT-2005-020841). ",
year = "2009",
month = sep,
doi = "10.1007/s00153-009-0143-5",
language = "English",
volume = "48",
pages = "679--690",
journal = "Archive for Mathematical Logic",
issn = "0933-5846",
publisher = "Springer New York",
number = "7",
}