MoL-2019-12: Henke, Tim (2019) The van Benthem Characterisation Theorem for Descriptive Models. [Report]
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Abstract
This thesis investigate the modal and first-order model theory of the class of models over descriptive general frames. Descriptive general frames are Stone spaces with a suitable relation over which every modal logic is complete. The main theorem of this thesis is the van Benthem Characterisation Theorem for the class of descriptive general models. Moreover, a model-theoretic analysis is given to prove that many important results from classical model theory, including the Compactness Theorem for first-order logic and the upward Löwenheim-Skolem Theorem, fail on the class of descriptive general models. The main tool developed in this thesis is the descriptive unravelling, a version of the unravelling tree that is modified to be descriptive. A careful analysis of the operation is provided and three isomorphic constructions are given: a construction through duality theorems, a construction through a topological toolkit based on nets that is also developed, and an explicit construction in terms of finite and infinite paths.
| Item Type: | Report |
|---|---|
| Report Nr: | MoL-2019-12 |
| Series Name: | Master of Logic Thesis (MoL) Series |
| Year: | 2019 |
| Subjects: | Logic Mathematics |
| Depositing User: | Dr Marco Vervoort |
| Date Deposited: | 19 Aug 2019 12:50 |
| Last Modified: | 19 Aug 2019 12:50 |
| URI: | https://eprints.illc.uva.nl/id/eprint/1702 |
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