Gödel’s Incompleteness Theorems

Serafim Batzoglou
Additional contact information
Serafim Batzoglou: Seer Inc.

Chapter Chapter 3 in Introduction to Incompleteness, 2024, pp 35-54 from Springer

Abstract: Abstract Gödel’s first incompleteness theorem holds a special place in the history of mathematics. In a popular list of the “top 100” theorems of all time, it ranks 6 th $${ }^{th}$$ , following the irrationality of 2 $$\sqrt {2}$$ , Gauss’s fundamental theorem of algebra, the countability of the rationals, the Pythagorean theorem, and the prime number theorem. And for good reason: for those expecting a foundation of mathematics on a defined collection of axioms from which all theorems are derived, the result must have been as startling as the discovery of 2 $$\sqrt {2}$$ by the Pythagoreans, who believed that all numbers are rational.

Date: 2024
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-64217-3_3

Ordering information: This item can be ordered from
http://www.springer.com/9783031642173

DOI: 10.1007/978-3-031-64217-3_3

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().