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SUMMARY:What is a forcing extension (of V)? - Barton\, N (University of Lo
 ndon)
DTSTART:20150824T123000Z
DTEND:20150824T130000Z
UID:TALK60434@talks.cam.ac.uk
CONTACT:42080
DESCRIPTION:Recent research into the representability of forcing extension
 s within ground models has often focussed on semantic formulations\; we fi
 nd definable class models within V that express very closely what it means
  to be a forcing extension of V (such as Hamkins' Naturalist Account of Fo
 rcing). In this paper\, I argue that while this formulation appears to be 
 a good candidate for interpreting forcing over V\, it is problematic in th
 at it is unable to interpret theorems concerning objects below a measurabl
 e cardinal whilst keeping the ultrapower well-founded\, and also encounter
 s difficulties in interpreting class forcings. Instead I suggest that the 
 motivation of a strong class theory (such as MK) over V\, combined with a 
 syntactic approach to forcing in a strengthened logic\, is able to provide
  an interpretation of various forcing constructions which does not encount
 er these difficulties.\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
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