arXiv math/97062081997-06math.LO

Coding into K by reasonable forcing

Ralf Schindler

英文摘要：

Assuming that there is no inner model with a strong cardinal, the following is shown: any subset of ω_1 can be made Δ^1_3 (in the codes) by a reasonable set-forcing; there is a reasonable set-generic extension with a Δ^1_3 well-ordering of its reals; 2-step Σ^1_4 absoluteness fails w.r.t. set-sized reasonable forcings.

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