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arXiv · 1701.07230

NS saturated and $Δ_1$-definable

Stefan Hoffelner
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Abstract

We show that under the assumption of the existence of the canonical inner model with one Woodin cardinal $M_1$, there is a model of $\ZFC$ in which $\NS$ is $\aleph_2$-saturated and $Δ_1$-definable with $ω_1$ as a parameter which answers a question of Sy-David Friedman and Liuzhen Wu. We also show that starting from an arbitrary universe with a Woodin cardinal, there is a model with $\NS$ saturated and $Δ_1$-definable with a ladder system $\vec{C}$ and a full Suslin tree $T$ as parameters. Both results rely on a new coding technique whose presentation is the main goal of this article.

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Stefan Hoffelner. 2021-12-15. NS saturated and $Δ_1$-definable. https://doi.org/10.1017/jsl.2021.23

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