20.500.12556/RUL-172003 Merljivi kardinali delo diplomskega seminarja Measurable cardinals Delo poveže obstoj mere iz analize in verjetnosti s filtri in kardinalnimi števili iz teorije množic. Najprej obravnava lastnosti dobrih urejenosti, ordinalov in kardinalov ter vpelje pojem transfinitne indukcije in rekurzije. Nato dokaže ekvivalenco med obstojem mere in obstojem ultrafiltra, kar privede do vpeljave merljivih kardinalov. Na koncu dokaže nedosegljivost merljivih kardinalov in jih poveže z drevesi in particijami iz kombinatorike. The work connects the existence of a measure from analysis and probability with filters and cardinal numbers from set theory. It first introduces the properties of well-orderings, ordinals, and cardinals, and introduces the concept of transfinite induction and recursion. It then proves the equivalence between the existence of a measure and the existence of an ultrafilter which leads to the introduction of measurable cardinals. Finally, it proves the inaccessibility of measurable cardinals and connects them to trees and partitions from combinatorics. merljiv kardinal mera ordinal dobra urejenost measurable cardinal measure ordinal well-ordering true false false Slovenski jezik Angleški jezik Delo diplomskega seminarja/zaključno seminarsko delo/naloga 2025-09-05 08:15:35 2025-09-05 08:15:36 2025-09-30 03:52:25 0000-00-00 00:00:00 2025 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 510.6 152608 247876099 19106.pdf 19106.pdf 1 2FF695623F89CB8AC301F02B0AA02513 274f5184c27cbaf8a15736e7b1a8d2b7fed83ac004a368cb3e2a050168fd615d 962f392b-8a1f-11f0-9328-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=215721 Fakulteta za matematiko in fiziko 0 0 0