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UncertaintyAjay
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So I just finished "Book of Proof" and I'm looking for a more rigourous book on axiomatic set theory, including Gödel's theorems.Any recommendations?
verty said:If you want set theory, I recall that Jech/Hrbacek is quite decent, if concise. Just don't accidentally get Jech's graduate book on set theory, that would be way too advanced.
If you want a wordier book, Suppes is nice because he proves every theorem in the book, so it's nice to try to prove them yourself to gain confidence.
Axiomatic Set Theory is a branch of mathematics that deals with the study of sets and their properties. It is based on a set of axioms, or fundamental principles, that serve as the foundation for all mathematical reasoning involving sets.
Axiomatic Set Theory is important because it provides a rigorous and formal framework for understanding sets and their properties. It also serves as the basis for many other areas of mathematics, such as topology, algebra, and analysis.
Some recommended books on Axiomatic Set Theory include "Introduction to Axiomatic Set Theory" by Gaisi Takeuti and Wilson M. Zaring, "Set Theory: An Introduction to Independence Proofs" by Kenneth Kunen, and "A Course in Mathematical Logic" by J. Shoenfield.
Books on Axiomatic Set Theory are primarily aimed at mathematicians and students of mathematics, particularly those interested in the foundations of mathematics and mathematical logic. However, anyone with a strong background in mathematics and a curiosity about the nature of sets may also find these books interesting and informative.
Yes, a solid understanding of mathematical concepts such as logic, proofs, and basic set theory is necessary before tackling books on Axiomatic Set Theory. Some familiarity with abstract algebra and topology may also be helpful. It is recommended to have at least a college-level mathematics background before diving into this subject.