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master's thesis
Kategorička logika
Zagreb: University of Zagreb, Faculty of Science, 2021. urn:nbn:hr:217:467030
Šestak, Teo
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Šestak, T. (2021). Kategorička logika (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:467030

Šestak, Teo. "Kategorička logika." Master's thesis, University of Zagreb, Faculty of Science, 2021. https://urn.nsk.hr/urn:nbn:hr:217:467030

Šestak, Teo. "Kategorička logika." Master's thesis, University of Zagreb, Faculty of Science, 2021. https://urn.nsk.hr/urn:nbn:hr:217:467030

Šestak, T. (2021). 'Kategorička logika', Master's thesis, University of Zagreb, Faculty of Science, accessed 03 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:467030

Šestak T. Kategorička logika [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2021 [cited 2024 November 03] Available at: https://urn.nsk.hr/urn:nbn:hr:217:467030

T. Šestak, "Kategorička logika", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2021. Available at: https://urn.nsk.hr/urn:nbn:hr:217:467030

Metadata
TitleKategorička logika
Title (english)Categorical logic
AuthorTeo Šestak
MentorIvan Tomašić (mentor)
MentorMladen Vuković (sumentor)
Committee memberMladen Vuković (predsjednik povjerenstva)
Committee memberIvan Tomašić (član povjerenstva)
Committee memberZvonko Iljazović (član povjerenstva)
Committee memberVedran Krčadinac (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2021-09-28, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu započinje se s osnovnim pojmovima teorije kategorija i teorije toposa s ciljem da se definira Grothendieckov topos. Također se definiraju klase kategorija koje koristimo za konstrukciju modela formalnih teorija. Uvodi se sekventni račun kao formalizacija izvoda i dokaza te se pomoću njega daje konstrukcija sintaktičke kategorije za geometrijske teorije. Takva kategorija sadrži generički model sa svojstvom da se ostali modeli mogu dobiti kao njegova slika. Rad završava konstrukcijom klasifikacijskog toposa, dokazom njegovog univerzalnog svojstva te se navodi kako konstruirati univerzalni model geometrijske teorije u njenom klasifikacijskom toposu.
Abstract (english)
In this thesis we begin by introducing some basics of category theory and topos theory in order to define the Grothendieck topos. We also define several classes of categories which are used to construct models of formal theories. Sequent calculus is introduced in order to formalize concepts of derivations and proofs. Using sequent calculus we also describe the construction of syntactic categories for geometric theories. Syntactic category contains the generic model such that other models can be expressed as images of the generic model. At the very end, the construction of classifying topos is is given, along with the proof of its universal property. We also show how to construct the universal model of a geometric theory inside its classifying topos.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:467030
Study programmeTitle: Pure Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2021-11-08 11:18:56