Dryaeva, Anastasia (2021) Topological Approach to Provability Logic. Bachelor's Thesis, Mathematics.
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Abstract
This thesis investigates the topological approach to provability logic, with a particular focus on the result proven by Leo Esakia in his 1981 article ``Diagonal Constructions, Löb’s Formula and Cantor’s Scattered Spaces''. Esakia's article discusses the interpretation of the modal diamond operator as the derived set operator on a topological space and proves that a topological space satisfies Löb’s axiom if and only if the space is scattered. This thesis gives a self-contained comprehensive overview of the topics from logic, algebra and topology required to understand this result, as well as a thorough and accessible proof. In the end, the application of this result to provability logic is made explicit, and an account of the impact the work by Esakia had on further developments in the field of mathematical logic is discussed.
| Item Type: | Thesis (Bachelor's Thesis) |
|---|---|
| Supervisor name: | Verbrugge, L.C. and Kiselev, A.V. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 08 Feb 2021 12:34 |
| Last Modified: | 08 Feb 2021 12:34 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/23933 |
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