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Reports Year : 2001

A Finite First-Order Presentation of Set Theory

Abstract

We present a first-order formalization of set theory which has a finite number of axioms. Its syntax is similar to that often used in textbooks: it provides an encoding of the comprehension symbol. We prove that this formalization is a "conservative extension" of Zermelo's set theory. In fact the proof is more general and applies to other variants of Zermelo's set theory like ZF. This formalization rests upon an encoding of the comprehension binder in a language of explicit substitution. This presentation of set theory is also described as a deduction modulo system and the proof of equivalence is done within this formalism.
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Dates and versions

inria-00072244 , version 1 (23-05-2006)

Identifiers

  • HAL Id : inria-00072244 , version 1

Cite

Stéphane Vaillant. A Finite First-Order Presentation of Set Theory. RR-4344, INRIA. 2001. ⟨inria-00072244⟩
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