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Abstract: Here we present a first-order formalization of set theory that has a finite number of axioms and which syntax is similar to the one often used in books: it provides an encoding of the comprehension symbol. Other formalizations of set theory exist: Zermelo theory with existence axioms is first-order but has no comprehension symbol and has an infinite number of axioms. (Update)
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BibTeX entry: (Update)
@misc{ vaillant-expressing,
author = "St\'ephane Vaillant",
title = "Expressing Set Theory in first-Order Predicate Logic",
url = "citeseer.ist.psu.edu/vaillant00expressing.html" }
Citations (may not include all citations):200 Introduction to mathematical logic (context) - Mendelson - 1987
24 Theorem proving modulo - Dowek, Hardin et al. - 1998
22 Proof normalization modulo - Dowek, Werner
5 uence properties of weak and strong calculi of explicit subs.. (context) - Curien, Hardin et al. - 1996
4 combinators and the comprehension scheme (context) - Dowek
3 rst-order calculus for higher-order calculi (context) - Pagano, eXplicit - 1998
1 rst-order logic: clauses for Gdel's axioms (context) - Boyer, Lusk et al. - 1986
1 Higher-order uni cation via explicit substitutions (context) - Dowek, Hardin et al. - 2000
1 rst-order expression of higher-order logic (context) - Dowek, Hardin et al.
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