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master's thesis
Quineovi ''Novi temelji'' teorije skupova
Zagreb: University of Zagreb, Faculty of Science, 2023. urn:nbn:hr:217:133180
Zlatunić, Gabrijela
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Zlatunić, G. (2023). Quineovi ''Novi temelji'' teorije skupova (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:133180

Zlatunić, Gabrijela. "Quineovi ''Novi temelji'' teorije skupova." Master's thesis, University of Zagreb, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:217:133180

Zlatunić, Gabrijela. "Quineovi ''Novi temelji'' teorije skupova." Master's thesis, University of Zagreb, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:217:133180

Zlatunić, G. (2023). 'Quineovi ''Novi temelji'' teorije skupova', Master's thesis, University of Zagreb, Faculty of Science, accessed 28 March 2025, https://urn.nsk.hr/urn:nbn:hr:217:133180

Zlatunić G. Quineovi ''Novi temelji'' teorije skupova [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2023 [cited 2025 March 28] Available at: https://urn.nsk.hr/urn:nbn:hr:217:133180

G. Zlatunić, "Quineovi ''Novi temelji'' teorije skupova", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:217:133180

Metadata
TitleQuineovi ''Novi temelji'' teorije skupova
Title (english)Quineovi ''Novi temelji'' teorije skupova
AuthorGabrijela Zlatunić
MentorVedran Čačić (mentor)
Committee memberVedran Čačić (predsjednik povjerenstva)
Committee memberMatej Mihelčić (član povjerenstva)
Committee memberGoranka Nogo (član povjerenstva)
Committee memberMarko Horvat (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2023-09-22, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Dajemo kratki pregled ovoga rada. Najprije uvodimo jezik teorije NF i sve osnovne pojmove na kojima je ona zasnovana. Zatim definiramo osnovne operacije na skupovima i uvodimo skupove od značaja poput skupa prirodnih brojeva i skupa kardinalnih brojeva. Želimo, barem ukratko, predstaviti ljepotu i gracioznost teorije NF zasnovane na jednostavnosti. Njena veličina ne bi bila upitna da nemamo drugo poglavlje - ono s druge strane preslikava sivu notu same teorije... More objašnjavajući, nadamo se dovoljno detaljno, zašto ista nije zaživjela, barem ne u svom prvotnom obliku. Težina Speckerovog teorema ne leži samo u dokazu (koliko god to bilo kontradiktorno veličini samog dokaza), nego i u posljedicama koje je tvrdnja imala na teoriju. Međutim, kako treće poglavlje da naslutiti, teorija je ipak bila dovoljno intrigantna i zanimljiva da je ovakav udarac nije slomio i bacio u zaborav. Tek nekolicina promjena u stvaranju jezika teorije rezultirala je (ne samo jednom) verzijom teorije koja ne samo da je relativno konzistentna s nekom već prihvaćenom teorijom u matematici, već ostaje konzistentnom i dodajući joj aksiom izbora i aksiom beskonačnosti - dvije tvrdnje nepomirljive u čistoj NF. Less
Abstract (english)
We provide a brief overview of this work. Firstly, we introduce the language of NF theory and all the fundamental concepts on which it is based. Then, we define basic operations on sets and introduce sets of significance such as the set of natural numbers and the set of cardinal numbers. We have attempted, at least briefly, to convey the beauty and elegance of NF theory based on its simplicity. Its magnitude would not be questionable if we did not have the second chapter, which, on... More the other hand, casts a shadow over the theory itself-explaining, hopefully in sufficient detail, why it has not caught on, at least not in its original form. The weight of Specker’s theorem lies not only in its proof (in spite of its size) but in the consequences its assertion has on the theory. However, as hinted at in the third chapter, the theory is intriguing and interesting enough that such a blow does not break it and send it to oblivion. Only a few changes in the formulation of the theory’s language result in multiple versions of the theory that are not only relatively consistent with previously accepted ones in mathematics, but also remain consistent when adding the axiom of choice and the axiom of infinity—two claims irreconcilable in pure NF. Less
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:133180
Study programmeTitle: Computer Science and Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: sveučilišni magistar računarstva i matematike (sveučilišni magistar računarstva i matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2024-02-07 12:30:59
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