Tennenbaum phenomena in models of arithmetic

• Thesis title in Czech: Tennenbaumův jev v modelech aritmetiky
• Thesis title in English: Tennenbaum phenomena in models of arithmetic
• Key words: teória modelov|Peanova aritmetika|teória vyčísliteľnosti|rekurzívne neštandardné modely|Tennenbaumova veta|typ usporiadania|div|mod
• English key words: model theory|Peano arithmetic|computability theory|recursive non-standard models|Tennenbaum's theorem|order-type|div|mod
• Academic year of topic announcement: 2022/2023
• Thesis type: Bachelor's thesis
• Thesis language: angličtina
• Department: Computer Science Institute of Charles University (32-IUUK)
• Supervisor: Neil Thapen
• Author: hidden - assigned and confirmed by the Study Dept.
• Date of registration: 19.07.2023
• Date of assignment: 19.07.2023
• Confirmed by Study dept. on: 31.07.2023
• Date and time of defence: 05.02.2024 10:00
• Date of electronic submission: 11.01.2024
• Date of submission of printed version: 11.01.2024
• Date of proceeded defence: 05.02.2024
• Opponents: RNDr. Jakub Bulín, Ph.D.

Guidelines

Tennenbaum's theorem shows that there is no computable nonstandard model of Peano
arithmetic. Give a presentation of it and investigate related questions, such as how weak a
theory of arithmetic can be used, or which aspects of the model can be made computable.

References

Richard Kaye. Models of Peano Arithmetic, Oxford University Press, 1991.