20.500.12556/RUL-184769 Novi temelji delo diplomskega seminarja New foundations V delu predstavimo aksiomatsko teorijo množic, imenovano Novi temelji. Najprej spoznamo osnovne aksiome in lastnosti ter si ogledamo nekaj pomembnih konstrukcij. V nadaljevanju definiramo kardinalna in ordinalna števila ter opišemo z njimi povezane rezultate. Obravnavamo aksiom štetja, dokažemo aksiom neskončnosti in ovržemo aksiom izbire. Dokažemo, da kategorija množic ni kartezično zaprta. Nazadnje dokažemo konsistentnost različice Novih temeljev z urelementi. In this thesis, we introduce the axiomatic set theory known as New foundations. Firstly, we define the basic axioms and properties and introduce some important constructions. Next, we define cardinal and ordinal numbers and state some results regarding them. We consider the axiom of counting, prove the axiom of infinity and disprove the axiom of choice. We prove that the category of sets is not Cartesian closed. Lastly, we prove the consistency of a variant of New foundations with urelements. Novi temelji aksiomatska teorija množic New foundations axiomatic set theory true false false Slovenski jezik Angleški jezik Diplomsko delo/naloga 2026-07-15 08:15:05 2026-07-15 08:15:08 2026-07-16 10:09:32 0000-00-00 00:00:00 2026 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 510.6 160662 285030403 22065.pdf 22065.pdf 1 D64ADCE9DFAA09663EEB7BFF25841BE6 01aa164210413ee279e1b9b0573e12d56bd4b28b19263dae9e91c25f54f5308b 594421ba-8014-11f1-9b0d-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=239969 Fakulteta za matematiko in fiziko 0 0 0