Mathias absoluteness and the Ramsey property

In this article we give a forcing characterization for the Ramsey property of Sigma-1-2 sets of reals. This research was motivated by the well-known forcing characterizations for Lebesgue measurability and the Baire property of Sigma-1-2 sets of reals. Further we will show tha relationship between higher degrees of forcing absoluteness and the Ramsey property of projective sets of reals.

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