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arXiv · 2311.02322

Adding highly undefinable sets over $L$

Mohammad Golshani·Saharon Shelah
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Abstract

We sow that there exists a generic extension of the G\"{o}del's constructible universe in which diamond holds and there exists a subset $Y \subseteq \omega_1$ such that for stationary many $\delta < \omega_1,$ the set $Y \cap \delta$ is not definable in the structure $(L_{F(\delta)}, \in)$, where $F(\delta) > \delta$ is the least ordinal such that $L_{F(\delta)}\models$``$\delta$ is countable''.

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Mohammad Golshani, Saharon Shelah. 2023-11-04. Adding highly undefinable sets over $L$. https://arxiv.org/abs/2311.02322

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