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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 Gödel's constructible universe in which diamond holds and there exists a subset $Y \subseteq ω_1$ such that for stationary many $δ< ω_1,$ the set $Y \cap δ$ is not definable in the structure $(L_{F(δ)}, \in)$, where $F(δ) > δ$ is the least ordinal such that $L_{F(δ)}\models$``$δ$ 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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