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SUMMARY:Forcing as a computational process - Joel David Hamkins (Oxford)
DTSTART:20190216T140000Z
DTEND:20190216T150000Z
UID:TALK119482@talks.cam.ac.uk
CONTACT:Benedikt Loewe
DESCRIPTION:We investigate the senses in which set-theoretic forcing can b
 e seen as a computational process on the models of set theory. Given an or
 acle 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-gener
 ic filters G⊂P∈M and the corresponding forcing extensions M[G]. Meanwh
 ile\, no such com­pu­ta­tio­nal process is functorial\, for there must
  always be isomorphic alternative presentations of the same model of set t
 heory M that lead by the computational process to non-isomorphic forcing e
 xtensions M[G]≆M[G′]. Indeed\, there is no Borel function providing ge
 neric filters that is functorial in this sense. This is joint work with Ru
 ssell Miller and Kameryn Williams.
LOCATION:Centre for Mathematical Sciences\, MR13
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