The Stratified Foundations as a Theory Modulo [chapter]

Gilles Dowek
2001 Lecture Notes in Computer Science  
The Strati ed Foundations are a restriction of naive set theory where the comprehension scheme is restricted to strati able propositions. It is known that this theory is consistent and that proofs strongly normalize in this theory. Deduction modulo is a formulation of rst-order logic with a general notion of cut. It is known that proofs normalize in a theory modulo if it has some kind of many-valued model called a pre-model. We show in this note that the Strati ed Foundations can be presented
more » ... deduction modulo and that the method used in the original normalization proof can be adapted to construct a pre-model for this theory.
doi:10.1007/3-540-45413-6_14 fatcat:t2qz4tgtkba2zorjqvhclphcrm