Abstract
We present a formalization of the axiomatic set theory ZF which reflects real mathematical practice, and is easy for mechanical manipulation and interactive theorem proving. Unlike the standard first-order formalizations, our version provides a rich class of abstraction terms denoting sets on the one hand, and is based on purely syntactical (rather than semantic) considerations on the other hand.
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References
Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. Addison-Wesley, Reading (1995)
Avron, A.: Transitive Closure and the Mechanization of Mathematics. In: Kamareddine, F. (ed.) Thirty Five Years of Automating Mathematics, pp. 149–171. Kluwer Academic Publishers, Dordrecht (2003)
Avron, A.: Safety Signatures for First-order Languages and Their Applications. In: Hendricks, et al. (eds.) First-Order Logic revisited. Logos Verlag, Berlin (2004)
Fraenkel, A., Bar-Hillel, Y., Levy, A.: Foundations of Set Theory. North-Holland, Amsterdam (1973)
Hallett, M.: Cantorian Set Theory and Limitation of Size. Clarendon Press, Oxford (1984)
Padlewska, B.: Families of Sets. Formalized Mathematics 1, 147–152 (1990)
Shoenfield, J.R.: Mathematical Logic. Addison-Wesley, Reading (1967)
Shoenfield, J.R.: Axioms of Set Theory. In: Barwise, J. (ed.) Handbook Of Mathematical Logic. North-Holland, Amsterdam (1977)
Ullman, J.D.: Principles of database and knowledge-base systems. Computer Science Press, Rockville (1988)
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© 2004 Springer-Verlag Berlin Heidelberg
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Avron, A. (2004). Formalizing Set Theory as it Is Actually Used. In: Asperti, A., Bancerek, G., Trybulec, A. (eds) Mathematical Knowledge Management. MKM 2004. Lecture Notes in Computer Science, vol 3119. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27818-4_3
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DOI: https://doi.org/10.1007/978-3-540-27818-4_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23029-8
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