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We examine some motivations for class-theoretic potentialism, before proving some results concerning the relevant potentialist systems (in particular exhibiting failures of the <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S1755020323000126_inline1.png\"\/><jats:tex-math>\n$\\mathsf {.2}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S1755020323000126_inline2.png\"\/><jats:tex-math>\n$\\mathsf {.3}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> axioms). We then discuss the significance of these results for the different kinds of class-theoretic potentialists.<\/jats:p>","DOI":"10.1017\/s1755020323000126","type":"journal-article","created":{"date-parts":[[2023,5,22]],"date-time":"2023-05-22T07:19:09Z","timestamp":1684739949000},"page":"272-304","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":2,"title":["VARIETIES OF CLASS-THEORETIC POTENTIALISM"],"prefix":"10.1017","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3637-1730","authenticated-orcid":false,"given":"NEIL","family":"BARTON","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"KAMERYN J.","family":"WILLIAMS","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2023,5,22]]},"reference":[{"key":"S1755020323000126_r12","doi-asserted-by":"publisher","DOI":"10.1111\/nous.12091"},{"volume-title":"Modal Logic","year":"2002","author":"Blackburn","key":"S1755020323000126_r3"},{"key":"S1755020323000126_r27","doi-asserted-by":"publisher","DOI":"10.1017\/S1755020318000242"},{"key":"S1755020323000126_r29","doi-asserted-by":"publisher","DOI":"10.1017\/jsl.2020.59"},{"key":"S1755020323000126_r32","doi-asserted-by":"publisher","DOI":"10.1017\/jsl.2016.4"},{"key":"S1755020323000126_r35","doi-asserted-by":"publisher","DOI":"10.2307\/2269948"},{"key":"S1755020323000126_r43","doi-asserted-by":"publisher","DOI":"10.2307\/2214641"},{"volume-title":"Parts of Classes","year":"1991","author":"Lewis","key":"S1755020323000126_r36"},{"key":"S1755020323000126_r18","doi-asserted-by":"publisher","DOI":"10.4064\/fm725-9-2020"},{"key":"S1755020323000126_r50","doi-asserted-by":"publisher","DOI":"10.2307\/2586799"},{"key":"S1755020323000126_r9","doi-asserted-by":"publisher","DOI":"10.1007\/BF01052728"},{"key":"S1755020323000126_r23","unstructured":"[21] Hamkins, J. 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