{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T06:22:33Z","timestamp":1780467753529,"version":"3.54.1"},"reference-count":48,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2021,11,22]],"date-time":"2021-11-22T00:00:00Z","timestamp":1637539200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/501100002261","name":"Russian Foundation for Basic Research","doi-asserted-by":"publisher","award":["20\u201031\u201070006"],"award-info":[{"award-number":["20\u201031\u201070006"]}],"id":[{"id":"10.13039\/501100002261","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004663","name":"Ministry of Science and Technology, Taiwan","doi-asserted-by":"publisher","award":["MOST\u00a0107\u20102410\u2010H\u2010194\u2010089\u2010MY3"],"award-info":[{"award-number":["MOST\u00a0107\u20102410\u2010H\u2010194\u2010089\u2010MY3"]}],"id":[{"id":"10.13039\/501100004663","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2022,2]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Mereological theories are based on the binary relation \u201cbeing a part of\u201d. The systematic investigations of mereology were initiated by Le\u015bniewski. More recent authors (including Simons, Casati and Varzi, Hovda) formulated a series of first\u2010order mereological axioms. These axioms give rise to a plenitude of theories, which are of great philosophical interest. The paper considers first\u2010order mereological theories from the point of view of computable (or effective) algebra. Following the approach of Hirschfeldt, Khoussainov, Shore, and Slinko, we isolate two important computability\u2010theoretic properties P (namely, degree spectra of structures, and effective dimensions), and consider the following problem: for a given mereological theory<jats:italic>T<\/jats:italic>, is it true that its models can realize every possible variant of the property P? If the answer is positive, then we say that the theory<jats:italic>T<\/jats:italic>is \u2010universal. We obtain the following results about known mereological theories. Any theory<jats:italic>T<\/jats:italic>which is weaker than Extensional Closure Mereology (CEM) is \u2010universal. A similar fact is true for the theory GM2. On the other hand, any theory stronger that CEM + (C) + (G) is not \u2010universal. In particular, General Extensional Mereology is not \u2010universal.<\/jats:p>","DOI":"10.1002\/malq.202100016","type":"journal-article","created":{"date-parts":[[2021,11,22]],"date-time":"2021-11-22T19:32:36Z","timestamp":1637609556000},"page":"48-66","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On the effective universality of mereological theories"],"prefix":"10.1002","volume":"68","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5834-2770","authenticated-orcid":false,"given":"Nikolay","family":"Bazhenov","sequence":"first","affiliation":[{"name":"Sobolev Institute of Mathematics 4 Acad. Koptyug Ave. Novosibirsk 630090 Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hsing\u2010Chien","family":"Tsai","sequence":"additional","affiliation":[{"name":"Department of Philosophy National Chung Cheng University No.168, Section\u00a01, University Road Min\u2010Hsiung Chia\u2010Yi 621301 Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2021,11,22]]},"reference":[{"key":"e_1_2_6_2_1","volume-title":"Computable Structures and the Hyperarithmetical Hierarchy","author":"Ash C. 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