Undecidability in algebra
The thesis first discusses first-order model theory and its key concepts, such as compactness, categoricity, and quantifier elimination. These concepts provide a method to construct complete theories. Afterwards, we examine the notion of incompleteness and Gödel's Incompleteness Theorems. Th...
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Nanyang Technological University
2024
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sg-ntu-dr.10356-1756482024-05-06T15:36:34Z Undecidability in algebra Ng, Kieran Elodie Wu Guohua School of Physical and Mathematical Sciences guohua@ntu.edu.sg Mathematical Sciences Incompleteness Undecidability First-order model theory The thesis first discusses first-order model theory and its key concepts, such as compactness, categoricity, and quantifier elimination. These concepts provide a method to construct complete theories. Afterwards, we examine the notion of incompleteness and Gödel's Incompleteness Theorems. The techniques used by Gödel to produce his incompleteness results will be discussed, as well as the various consequences. In particular, we will look at two independence results in Peano Arithmetic, Goodstein’s Theorem, and the Paris-Harrington Principle. Finally, the thesis will also touch on the basics on computability theory. This includes the Church-Turing Thesis and the Halting Problem. An application of undecidability will also be examined, in the form of groups with unsolvable word problems. Bachelor's degree 2024-05-02T05:33:41Z 2024-05-02T05:33:41Z 2024 Final Year Project (FYP) Ng, K. E. (2024). Undecidability in algebra. Final Year Project (FYP), Nanyang Technological University, Singapore. https://hdl.handle.net/10356/175648 https://hdl.handle.net/10356/175648 en application/pdf Nanyang Technological University |
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Nanyang Technological University |
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NTU Library |
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Asia |
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Singapore Singapore |
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NTU Library |
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English |
| topic |
Mathematical Sciences Incompleteness Undecidability First-order model theory |
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Mathematical Sciences Incompleteness Undecidability First-order model theory Ng, Kieran Elodie Undecidability in algebra |
| description |
The thesis first discusses first-order model theory and its key concepts, such as compactness,
categoricity, and quantifier elimination. These concepts provide a method to construct complete
theories. Afterwards, we examine the notion of incompleteness and Gödel's Incompleteness
Theorems. The techniques used by Gödel to produce his incompleteness results will be discussed,
as well as the various consequences. In particular, we will look at two independence results in
Peano Arithmetic, Goodstein’s Theorem, and the Paris-Harrington Principle. Finally, the thesis
will also touch on the basics on computability theory. This includes the Church-Turing Thesis
and the Halting Problem. An application of undecidability will also be examined, in the form
of groups with unsolvable word problems. |
| author2 |
Wu Guohua |
| author_facet |
Wu Guohua Ng, Kieran Elodie |
| format |
Final Year Project |
| author |
Ng, Kieran Elodie |
| author_sort |
Ng, Kieran Elodie |
| title |
Undecidability in algebra |
| title_short |
Undecidability in algebra |
| title_full |
Undecidability in algebra |
| title_fullStr |
Undecidability in algebra |
| title_full_unstemmed |
Undecidability in algebra |
| title_sort |
undecidability in algebra |
| publisher |
Nanyang Technological University |
| publishDate |
2024 |
| url |
https://hdl.handle.net/10356/175648 |
| _version_ |
1800916187395129344 |