Relative definability and models of unary PCF

Authors:
Antonio Bucciarelli;Benjamin Leperchey;Vincent Padovani
Affiliations:
PPS, Université Denis Diderot, Paris;PPS, Université Denis Diderot, Paris;PPS, Université Denis Diderot, Paris
Venue:
TLCA'03 Proceedings of the 6th international conference on Typed lambda calculi and applications
Year:
2003

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Abstract

We show that the poset of degrees of relative definability in the Scott model of Unary PCF is non trivial, and that, nevertheless, the hierarchy of order extensional models of the language is reduced to a bottom element (the fully abstract model) and a top one (the Scott model itself).