Amoeba-absoluteness and projective measurability

Journal of Symbolic Logic 58 (4):1284-1290 (1993)
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Abstract

We show that Σ1 4-Amoeba-absoluteness implies that $\forall a \in \mathbb{R}(\omega^{L\lbrack a \rbrack}_1 < \omega^V_1)$ and, hence, Σ1 3-measurability. This answers a question of Haim Judah (private communication)

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Citations of this work

Forcing absoluteness and regularity properties.Daisuke Ikegami - 2010 - Annals of Pure and Applied Logic 161 (7):879-894.
Combinatorial properties of classical forcing notions.Jörg Brendle - 1995 - Annals of Pure and Applied Logic 73 (2):143-170.
Projective absoluteness for Sacks forcing.Daisuke Ikegami - 2009 - Archive for Mathematical Logic 48 (7):679-690.

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References found in this work

Set Theory.Thomas Jech - 1999 - Studia Logica 63 (2):300-300.
Δ12-sets of reals.Jaime I. Ihoda & Saharon Shelah - 1989 - Annals of Pure and Applied Logic 42 (3):207-223.
Combinatorial properties of Hechler forcing.Jörg Brendle, Haim Judah & Saharon Shelah - 1992 - Annals of Pure and Applied Logic 58 (3):185-199.
DELTA ¹2-sets of reals.J. I. Ihoda - 1989 - Annals of Pure and Applied Logic 42 (3):207.

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