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  1. Projective absoluteness for Sacks forcing.Daisuke Ikegami - 2009 - Archive for Mathematical Logic 48 (7):679-690.
    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.
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  • Mathias and set theory.Akihiro Kanamori - 2016 - Mathematical Logic Quarterly 62 (3):278-294.
    On the occasion of his 70th birthday, the work of Adrian Mathias in set theory is surveyed in its full range and extent.
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  • Forcing absoluteness and regularity properties.Daisuke Ikegami - 2010 - Annals of Pure and Applied Logic 161 (7):879-894.
    For a large natural class of forcing notions, we prove general equivalence theorems between forcing absoluteness statements, regularity properties, and transcendence properties over and the core model . We use our results to answer open questions from set theory of the reals.
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