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Projective absoluteness under Sacks forcing
"... Abstract. We show that Σ 1 3-absoluteness under Sacks forcing is equivalent to the Sacks measurability of every ∆ 1 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 Σ 1 3 forcing absoluteness. 1. ..."
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Abstract. We show that Σ 1 3-absoluteness under Sacks forcing is equivalent to the Sacks measurability of every ∆ 1 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 Σ 1 3 forcing absoluteness. 1.
