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Log."],"published-print":{"date-parts":[[2025,12]]},"abstract":"<jats:p>A first-order theory is Noetherian with respect to the collection of formulae [Formula: see text] if every definable set is a Boolean combination of instances of formulae in [Formula: see text] and the topology whose subbasis of closed sets is the collection of instances of arbitrary formulae in [Formula: see text] is Noetherian. We show the Noetherianity of the theory of proper pairs of algebraically closed fields in any characteristic with respect to the family of tame formulae as introduced in [A. Martin-Pizarro and M. Ziegler, Equational theories of fields, J. Symbolic Logic\u00a085 (2020) 828\u2013851, https:\/\/arxiv.org\/abs\/1702.05735 ], thus answering a question which was left open there.<\/jats:p>","DOI":"10.1142\/s0219061324500247","type":"journal-article","created":{"date-parts":[[2024,8,23]],"date-time":"2024-08-23T04:38:42Z","timestamp":1724387922000},"source":"Crossref","is-referenced-by-count":0,"title":["Noetherian theories"],"prefix":"10.1142","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7739-5096","authenticated-orcid":false,"given":"Amador","family":"Martin-Pizarro","sequence":"first","affiliation":[{"name":"Mathematisches Institut, Albert-Ludwigs-Universit\u00e4t Freiburg, D-79104 Freiburg, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Martin","family":"Ziegler","sequence":"additional","affiliation":[{"name":"Mathematisches Institut, Albert-Ludwigs-Universit\u00e4t Freiburg, D-79104 Freiburg, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2024,10,7]]},"reference":[{"key":"S0219061324500247BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-0072(03)00018-6"},{"key":"S0219061324500247BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-0072(99)00034-2"},{"key":"S0219061324500247BIB003","doi-asserted-by":"publisher","DOI":"10.1142\/S179374421250003X"},{"key":"S0219061324500247BIB004","unstructured":"J. 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