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Forcing as a computational process

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If you have a question about this talk, please contact Benedikt Loewe.

part of STUK 1

We investigate the senses in which set-theoretic forcing can be seen as a computational process on the models of set theory. Given an oracle for the atomic or elementary diagram of a model of set theory ⟨M,∈M⟩, for example, we explain senses in which one may compute M-generic filters G⊂P∈M and the corresponding forcing extensions M[G]. Meanwhile, no such com­pu­ta­tio­nal process is functorial, for there must always be isomorphic alternative presentations of the same model of set theory M that lead by the computational process to non-isomorphic forcing extensions M[G]≆M[G′]. Indeed, there is no Borel function providing generic filters that is functorial in this sense. This is joint work with Russell Miller and Kameryn Williams.

This talk is part of the Set Theory Seminar series.

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