Fionn, Donoghue (2025) Model theoretic consistency of transfinite induction. Bachelor's Thesis, Mathematics.
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Abstract
In this thesis we explore model-theoretic methods of determining the validity of the proof technique and logical inference tool known as transfinite induction. We explore basic model theory and specific theories therein, such as Peano Arith- metic and its arithmetic Hierarchy of formulas as well as Zermelo-Frankel- Choice set theory. In those theories, we show the validity of transfinite indu- ction in fragments of PA, as well as the validity of ϵ-induction and transfinite induction in ZFC. We also provide the context and necessary conditions for the use of transfinite induction in general mathematics.
| Item Type: | Thesis (Bachelor's Thesis) |
|---|---|
| Supervisor name: | Verbrugge, L.C. and Top, J. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 21 Jul 2025 14:03 |
| Last Modified: | 21 Jul 2025 14:03 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/36429 |
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