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 in one of its arguments we let the given formalization rest upon a calculus of explicit substitution with de Bruijn indices. This presentation of 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.
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Vaillant, S. (2003). A Finite First-Order Presentation of Set Theory. In: Geuvers, H., Wiedijk, F. (eds) Types for Proofs and Programs. TYPES 2002. Lecture Notes in Computer Science, vol 2646. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-39185-1_18
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DOI: https://doi.org/10.1007/3-540-39185-1_18
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