Abstract

In this chapter, we shall present and discuss the axioms of Zermelo-Fraenkel Set Theory including the Axiom of Choice, denoted ZFC. It will turn out that within this axiom system, we can develop all of first-order mathematics, and therefore, the axiom system ZFC serves as a foundation of mathematics.

Full Text
Published version (Free)

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Similar Papers

Paper Title
Journal
Date
Author
A Formal System of Axiomatic Set Theory in Coq
Wensheng Yu ... Tianyu Sun
IEEE Access | VOL. 8
Wensheng Yu, et. al.Wensheng Yu ... Tianyu Sun
27 Jan 2020
Some proofs of independence in axiomatic set theory
Elliott Mendelson
Journal of Symbolic Logic | VOL. 21
Elliott MendelsonElliott Mendelson
01 Sep 1956
George Boolos. The iterative conception of set. The journal of philosophy, vol. 68 (1971), pp. 215–231. - Dana Scott. Axiomatizing set theory. Axiomatic set theory, edited by Thomas J. Jech, Proceedings of symposia in pure mathematics, vol. 13 part 2, American Mathematical Society, Providence1974, pp. 207–214. - W. N. Reinhardt. Remarks on reflection principles, large cardinals, and elementary embeddings. Axiomatic set theory, edited by Thomas J. Jech, Proceedings of symposia in pure mathematics, vol. 13 part 2, American Mathematical Society, Providence1974, pp. 189–205. - W. N. Reinhardt. Set existence principles of Shoenfield, Ackermann, and Powell. Fundament a mathematicae, vol. 84 (1974), pp. 5–34. - Hao Wang. Large sets. Logic, foundations of mathematics, and computahility theory. Part one of the proceedings of the Fifth International Congress of Logic, Methodology and Philosophy of Science, London, Ontario, Canada–1975, edited by Robert E. Butts and Jaakko Hintikka, The University of Western Ontario series in philosophy of science, vol. 9, D. Reidel Publishing Company, Dordrecht and Boston1977, pp. 309–333. - Charles Parsons. What is the iterative conception of set?Logic, foundations of mathematics, and computahility theory. Part one of the proceedings of the Fifth International Congress of Logic, Methodology and Philosophy of Science, London, Ontario, Canada–1975, edited by Robert E. Butts and Jaakko Hintikka, The University of Western Ontario series in philosophy of science, vol. 9, D. Reidel Publishing Company, Dordrecht and Boston1977, pp. 335–367.
John P. Burgess
Journal of Symbolic Logic | VOL. 50
John P. BurgessJohn P. Burgess
01 Jun 1985
Sharon Berry.A Logical Foundation for Potentialist Set Theory
Chris Scambler
Philosophia Mathematica | VOL. 31
Chris ScamblerChris Scambler
20 Feb 2023
View more papers