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Proving Godel's Theorem, a set-theoretical approach

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Date Issued:
2020
Abstract/Description:
Before Godel's incompleteness theorems, logicians such as Bertrand Russel and Alfred Whitehead pursued an ideal axiomatic system which would have created a reliable framework to successfully prove or refute every mathematical sentence. Godel proved that such systems can never be created. In fact, Godel's incompleteness theorems establish that axiomatic systems that are complex enough to formulate arithmetic can never generate a proof of all the logical statements that are expressible inside of them. According to the first incompleteness theorem, there are constructible mathematical sentences that can never be proven to be true or false using the axioms and the logical rules of the system. Furthermore, the second incompleteness theorem argues that the consistency of all axiomatic systems which contain Peano or Robinson arithmetic can never be determined using the rules and the proof mechanisms available in the system.
Title: Proving Godel's Theorem, a set-theoretical approach.
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Name(s): Lohier, Jean, author
McGovern, Warren, Thesis advisor
Florida Atlantic University
Harriet L. Wilkes Honors College
Type of Resource: text
Genre: Thesis
Date Created: 2020
Date Issued: 2020
Publisher: Florida Atlantic University Digital Library
Place of Publication: Boca Raton, Fla.
Physical Form: online resource
Extent: 27 p.
Language(s): English
Abstract/Description: Before Godel's incompleteness theorems, logicians such as Bertrand Russel and Alfred Whitehead pursued an ideal axiomatic system which would have created a reliable framework to successfully prove or refute every mathematical sentence. Godel proved that such systems can never be created. In fact, Godel's incompleteness theorems establish that axiomatic systems that are complex enough to formulate arithmetic can never generate a proof of all the logical statements that are expressible inside of them. According to the first incompleteness theorem, there are constructible mathematical sentences that can never be proven to be true or false using the axioms and the logical rules of the system. Furthermore, the second incompleteness theorem argues that the consistency of all axiomatic systems which contain Peano or Robinson arithmetic can never be determined using the rules and the proof mechanisms available in the system.
Identifier: FA00003715 (IID)
Degree granted: Thesis (B.A.)--Florida Atlantic University, Harriet L. Wilkes Honors College, 2020.
Collection: Florida Atlantic University Digital Library Collections
Note(s): Includes bibliography.
Persistent Link to This Record: http://purl.flvc.org/fau/fd/FA00003715
Use and Reproduction: Copyright © is held by the author with permission granted to Florida Atlantic University to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Use and Reproduction: http://rightsstatements.org/vocab/InC/1.0/
Host Institution: FAU

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