Skupovne interpretacije modalne logike

Kiršek, Filip (2016) Skupovne interpretacije modalne logike. Diploma thesis, Faculty of Science > Department of Mathematics.

Language: Croatian

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Modal logic is concerned with the notions of necessity and possibility. This thesis defines the modal systems K, K4, GL and I, and contains proofs of soundness and completeness theorems of those systems in standard Kripkean semantics. The axioms of the Zermelo-Fraenkel set theory are then presented, and the notions of relativizations and transitive models of ZF are defined. The idea behind Gödel numbering of PA and ZF formulas is presented as well. Using those notions, the idea of formalizing the method of ZF proving relative consistency and independence of its axioms is described. Finally, Solovay's theorems of arithmetical completeness for modal systems GL, GLS, I and J are then presented, and a rough overview of the proof of arithmetical completeness of system I, concerning transitive models of ZF, is explored. The notion of forcing, among other ideas, is needed for completing the proof.

Item Type: Thesis (Diploma thesis)
Supervisor: Vuković, Mladen
Date: 2016
Number of Pages: 49
Subjects: NATURAL SCIENCES > Mathematics
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 26 Oct 2016 10:56
Last Modified: 26 Oct 2016 10:56

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