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master's thesis
Skupovne interpretacije modalne logike
Zagreb: University of Zagreb, Faculty of Science, 2016. urn:nbn:hr:217:846037
Kiršek, Filip
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Kiršek, F. (2016). Skupovne interpretacije modalne logike (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:846037

Kiršek, Filip. "Skupovne interpretacije modalne logike." Master's thesis, University of Zagreb, Faculty of Science, 2016. https://urn.nsk.hr/urn:nbn:hr:217:846037

Kiršek, Filip. "Skupovne interpretacije modalne logike." Master's thesis, University of Zagreb, Faculty of Science, 2016. https://urn.nsk.hr/urn:nbn:hr:217:846037

Kiršek, F. (2016). 'Skupovne interpretacije modalne logike', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:846037

Kiršek F. Skupovne interpretacije modalne logike [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2016 [cited 2024 November 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:846037

F. Kiršek, "Skupovne interpretacije modalne logike", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2016. Available at: https://urn.nsk.hr/urn:nbn:hr:217:846037

Metadata
TitleSkupovne interpretacije modalne logike
AuthorFilip Kiršek
MentorMladen Vuković (mentor)
Committee memberMladen Vuković (predsjednik povjerenstva)
Committee memberVedran Čačić (član povjerenstva)
Committee memberTin Perkov (član povjerenstva)
Committee memberFranka Miriam Bruckler (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2016-09-26, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Modalna logika se bavi idejama nužnosti i mogućnosti. U ovom radu definiramo modalne sustave K, K4, GL i I, te dokazujemo standardne teoreme adekvatnosti i potpunosti tih sustava sa Kripkeovom semantikom. Zatim ponovno predstavljamo aksiome Zermelo-Fraenkelove teorije skupova, te uvodimo pojam relativizacije formule, te pojam tranzitivnih modela. Potom predstavljamo pregled ideje Gödelove aritmetizacije sustava Peanovih aksioma i Zermelo-Fraenkelove teorije skupova. Koristeći te pojmove razmatramo kako teorija ZF može govoriti o dokazivosti te relativnoj nezavisnosti i konzistentnosti svojih aksioma. Konačno, iskazujemo Solovayeve teoreme aritmetičke potpunosti za modalne sustave GL, GLS, I i J, te predstavljamo skicu dokaza aritmetičke potpunosti za sustav I. Za upotpunjavanje te skice dokaza je potrebna, među ostalima, metoda forcinga.
Abstract (english)
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.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:846037
Study programmeTitle: Computer Science and Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra računarstva i matematike (magistar/magistra računarstva i matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-02-12 12:39:57