Mathias absoluteness and the Ramsey property

Journal of Symbolic Logic 61 (1):177-194 (1996)
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Abstract

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

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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.
Mathias and set theory.Akihiro Kanamori - 2016 - Mathematical Logic Quarterly 62 (3):278-294.
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

Happy families.A. R. D. Mathias - 1977 - Annals of Mathematical Logic 12 (1):59.
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.
Exact equiconsistency results for Δ 3 1 -sets of reals.Haim Judah - 1992 - Archive for Mathematical Logic 32 (2):101-112.

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