Σ 3 1 absoluteness and the second uniform indiscernible
Tóm tắt
We show that that if every real has a sharp and there are Δ
2
1
-definable prewellorderings of ℝ of ordinal ranks unbounded inω
2, then there is an inner model for a strong cardinal. Similarly, assuming the same sharps, the Core ModelK is Σ
3
1
-absolute unless there is an inner model for a strong cardinal.
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