Annals of Pure and Applied Logic 89 (1):93-99 (1997)

We isolate a condition on a class A of ordinals sufficient to Δ1-code it by a real in a class-generic extension of L. We then apply this condition to show that the class of ordinals of L-cofinality ω is Δ1 in a real of L-degree strictly below O#
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DOI 10.1016/s0168-0072(96)00023-1
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Coding the Universe.A. Beller, R. Jensen & P. Welch - 1982 - Cambridge University Press.
Proper Forcing.Saharon Shelah - 1985 - Journal of Symbolic Logic 50 (1):237-239.

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