Amoeba-absoluteness and projective measurability

Details Amoeba-absoluteness and projective measurability Amoeba-absoluteness and projective measurability

1992-09-15

arxiv.org/abs/math/9209206v1

Mathematics

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Scientific paper

We study the relationship between Amoeba forcing (the partial order which generically adds a measure one set of random reals) and projective measurability. Given a universe V of set theory and a forcing notion P in V we say that V is Sigma^1_n - P - absolute iff for every Sigma^1_n-sentence phi with parameters in V we have V models phi iff V^P models phi. We show that Sigma^1_4-Amoeba-absoluteness implies that forall a in omega^omega (omega_1^{L[a]} < omega_1^V), and hence Sigma^1_3-measurability. This answers a question of Haim Judah (private communication).

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