Tripos theory in retrospect
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by Andrew M. P I Tts
ftp://ftp.cl.cam.ac.uk/papers/amp12/tritr.ps.gz
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Abstract:
explain in what sense Higg's description of sheaf toposes as H-valued sets and Hyland's realizability toposes are instances of the same construction. The construction itself can be seen as the universal solution to the problem of realizing the predicates of a first order hyperdoctrine as subobjects in a logos with effective equivalence relations. In this note it is shown that the resulting logos is actually a topos if and only if the original hyperdoctrine satisfies a certain comprehension property. Triposes satisfy this property, but there are examples of non-triposes satisfying this form of comprehension. 1.
Citations
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| 44 | Realizability Toposes and Language Semantics – Longley - 1995 |
| 38 | Sheaves and logic – Fourman, Scott - 1979 |
| 30 | A small complete category – Hyland - 1988 |
| 20 | Local realizability toposes and a modal logic for computability – Awodey, Birkedal, et al. - 1999 |
| 14 | Adjointness in foundations – Lawvere - 1969 |
| 7 | The fibrational formulation of intuitionistic predicate logic I: completeness according to Godel – Makkai - 1993 |
| 2 | Tutorial Workshop on Realizability Semantics – Birkedal, Rosolini - 1999 |
| 1 | Topos Theory. Number 10 in LMS Mathematical Monographs – Johnstone - 1977 |
