A finite first-order presentation of set theory

Authors:
Stéphane Vaillant
Affiliations:
INRIA-Futurs, Le Chesnay Cedex, France
Venue:
TYPES'02 Proceedings of the 2002 international conference on Types for proofs and programs
Year:
2002

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Abstract

We present a first-order formalization of set theory which has a finite number of axioms. Its syntax is familiar since it provides an encoding of the comprehension symbol. Since this symbol binds a variable inon e of its arguments we let the givenformalizationrest upona calculus of explicit substitutionwith de Bruijnin dices. This presentationof set theory is also described as a deduction modulo system which is used as an intermediate system to prove that the given presentation is a conservative extension of Zermelo's set theory.