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arXiv · 1807.02206

On forcing projective generic absoluteness from strong cardinals

Trevor M. Wilson
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Abstract

W.H. Woodin showed that if $\kappa_1 < \cdots < \kappa_n$ are strong cardinals then two-step ${\bf\Sigma}^1_{n+3}$ generic absoluteness holds after collapsing $2^{2^{\kappa_n}}$ to be countable. We show that this number can be reduced to $2^{\kappa_n}$, and to $\kappa_n^+$ in the case $n = 1$, but cannot be further reduced to $\kappa_n$.

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Trevor M. Wilson. 2018-07-06. On forcing projective generic absoluteness from strong cardinals. https://arxiv.org/abs/1807.02206

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