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me tutvustame lühidalt zorn osaluse algebra ja hulgateooria. olgem nüüd lühike ülevaade oma panuse analüüsi.
we have looked briefly at zorn's contributions to algebra and to set theory. let us now take a brief look at his contributions to analysis.
kui üks on eraldi välja üks intrigeerivamaid punktis, oleks arvatavasti oma töö standardist erinev mudelid hulgateooria ja mitmeid teooria.
if one has to single out one most intriguing item, it would probably be his work on nonstandard models of set theory and number theory.
bendixson avaldas need tulemused acta mathematica ja väärib märkimist, et ta oli valmis aktsepteerima uusi ideid hulgateooria kuid mitte grupi teooria.
bendixson published these results in acta mathematica and it is worth noticing that he was prepared to accept the new ideas of set theory but not of group theory.
see oli mitte ainult tulemuse, mis oli oluline määrata teoreetiliselt, vaid ka meetodeid, mis aleksandrov kasutada mis osutus üheks kõige kasulikumaks meetodeid kirjeldav hulgateooria.
it was not only the result which was important for set theory, but also the methods which aleksandrov used which turned out to be one of the most useful methods in descriptive set theory.
1926 finsler toodetud esimese osa suur töö esitatud teooria alused hulgateooria. kavatseb ta avaldada teine osa on järg tema teooriaid, kuid tema kava muuta, kui esimene osa tuli rünnaku alla.
in 1926 finsler produced the first part of a major work on set theory on the foundations of set theory. he intended to publish the second part as a continuation of his theories but his plan changed when the first part came under attack.
ta võttis russell 's eemaldatakse lahusest loogiline paradokse hulgateooria tulenevad näiteks "sätestatud kõikide hulkade, kes ei ole iseenesest".
he accepted russell 's solution to remove the logical paradoxes of set theory arising from, for example, "the set of all sets which are not members of themselves".
kirjavahetus mittag-leffler ja cantor kõik, kuid loobus varsti pärast seda sündmust ja üleujutuste uusi ideid, mis tõi kaasa cantori kiire areng hulgateooria üle umbes 12 aastat tundub olevat peaaegu seiskus.
the correspondence between mittag-leffler and cantor all but stopped shortly after this event and the flood of new ideas which had led to cantor's rapid development of set theory over about 12 years seems to have almost stopped.
[ kuratowski ] andis elementaarne kursuse hulgateooria ja küsisin mõned küsimused, siis ma rääkisin temaga pärast klasside lõikes, ja ta sai huvitatud noor üliõpilane, kes ilmselt oli huvitatud matemaatika ja olid mõned mõtted. ma olin õnnelik, et lahendada lahendamata probleem, mis tegi ta ettepaneku.
[ kuratowski ] gave an elementary course on set theory, and i asked some questions, then i talked to him after classes, and he became interested in a young student who evidently was interested in mathematics and had some ideas. i was lucky to solve an unsolved problem that he proposed.