• Corpus ID: 220280398

Forcing as a computational process

@article{Hamkins2020ForcingAA,
  title={Forcing as a computational process},
  author={Joel David Hamkins and Russell G. Miller and Kameryn J. Williams},
  journal={arXiv: Logic},
  year={2020}
}
We investigate how set-theoretic forcing can be seen as a computational process on the models of set theory. Given an oracle for information about a model of set theory $\langle M,\in^M\rangle$, we explain senses in which one may compute $M$-generic filters $G\subseteq\mathbb{P}\in M$ and the corresponding forcing extensions $M[G]$. Specifically, from the atomic diagram one may compute $G$, from the $\Delta_0$-diagram one may compute $M[G]$ and its $\Delta_0$-diagram, and from the elementary… 

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