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We generalize fundamental results from the countable to the uncountable, but often in surprisingly strengthened forms, and present models with varying structures of the cofinal types of ultrafilters over measurable cardinals.<\/jats:p>","DOI":"10.1017\/jsl.2024.12","type":"journal-article","created":{"date-parts":[[2024,2,28]],"date-time":"2024-02-28T03:58:11Z","timestamp":1709092691000},"page":"1801-1835","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":2,"title":["COFINAL TYPES OF ULTRAFILTERS OVER MEASURABLE CARDINALS"],"prefix":"10.1017","volume":"90","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4100-6524","authenticated-orcid":false,"given":"TOM","family":"BENHAMOU","sequence":"first","affiliation":[{"name":"UNIVERSITY OF ILLINOIS AT CHICAGO"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"NATASHA","family":"DOBRINEN","sequence":"additional","affiliation":[{"name":"UNIVERSITY OF NOTRE 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