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SUMMARY:Characterising realisability toposes - Jonas Frey\, Paris
DTSTART:20120508T131500Z
DTEND:20120508T141500Z
UID:TALK37990@talks.cam.ac.uk
CONTACT:Julia Goedecke
DESCRIPTION:In this talk\, I will give a characterisation of realisability
  toposes over partial combinatory algebras. More precisely\, we do not cha
 racterise the bare toposes\, but the toposes together with the associated 
 'constant objects functor' Delta: Set -> RT(A) for a partial combinatory a
 lgebra A. By Moens' theorem\, such a functor\nis equivalent to a fibering 
 of RT(A) over Set (given via glueing).\n\nOur approach is to view realisab
 ility toposes as generalised presheaf toposes\, where the underlying categ
 ory is replaced by an underlying fibration. As in the non-fibred case\, th
 ese generalised presheaf toposes can be characterised in terms of indecomp
 osable projectives. To obtain a characterisation of realisability over a p
 artial combinatory algebra\, it remains to characterise the fibrations tha
 t are induced by pcas. This is achieved using techniques introduced by\nHo
 fstra and Longley in their work on categories of 'combinatory objects'.
LOCATION:MR5\, Centre for Mathematical Sciences
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