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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, $\Theta_0$ of the derived model at $\kappa$ is below $\kappa^+$. 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 $\Theta < \kappa^+$ 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. 2025-01-10. Derived Models in PFA. https://arxiv.org/abs/2501.05954

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