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arXiv · 2501.05954

Derived Models in PFA

Derek Levinson·Nam Trang
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Abstract

We discuss a conjecture of Wilson that under the proper forcing axiom, $Θ_0$ of the derived model at $κ$ is below $κ^+$. We prove the conjecture holds for the old derived model. Assuming mouse capturing in the new derived model, the conjecture holds there as well. We also show $Θ< κ^+$ in the case of the old derived model, and under additional hypotheses for the new derived model.

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Derek Levinson, Nam Trang. 2025-07-17. Derived Models in PFA. https://arxiv.org/abs/2501.05954

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