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The principle <jats:italic>Maximum Deconstructibility (MD)<\/jats:italic> asserts that a certain necessary condition for a class to be deconstructible is also sufficient. MD implies, for example, that the classes of Gorenstein Projective modules, Ding Projective modules, their relativized variants, and all torsion classes are deconstructible over any ring. MD was known to follow from Vop\u011bnka\u2019s Principle and imply the existence of an <jats:inline-formula>\n              <jats:tex-math>$$\\omega _1$$<\/jats:tex-math>\n            <\/jats:inline-formula>-strongly compact cardinal. We prove that MD is equivalent to Vop\u011bnka\u2019s Principle, and to the assertion that each torsion class of abelian groups is generated by a single group within the class (yielding the converse of a theorem of G\u00f6bel and Shelah).<\/jats:p>","DOI":"10.1007\/s10485-025-09814-2","type":"journal-article","created":{"date-parts":[[2025,5,31]],"date-time":"2025-05-31T09:51:00Z","timestamp":1748685060000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Vop\u011bnka\u2019s Principle, Maximum Deconstructibility, and Singly-Generated Torsion Classes"],"prefix":"10.1007","volume":"33","author":[{"given":"Sean","family":"Cox","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,5,31]]},"reference":[{"key":"9814_CR1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511600579","volume-title":"Locally presentable and accessible categories, London Mathematical Society Lecture Note Series, 189","author":"J Ad\u00e1mek","year":"1994","unstructured":"Ad\u00e1mek, J., Rosick\u00fd, J.: Locally presentable and accessible categories, London Mathematical Society Lecture Note Series, 189. 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