{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T14:26:58Z","timestamp":1759847218556},"reference-count":18,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","funder":[{"name":"Ministerio de Economia, Industria y Competitividad, Spain","award":["MTM2014-59178P"],"award-info":[{"award-number":["MTM2014-59178P"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Math. Log."],"published-print":{"date-parts":[[2020,8]]},"abstract":"<jats:p>A Steiner triple system (STS) is a set [Formula: see text] together with a collection [Formula: see text] of subsets of [Formula: see text] of size 3 such that any two elements of [Formula: see text] belong to exactly one element of [Formula: see text]. It is well known that the class of finite STS has a Fra\u00efss\u00e9 limit [Formula: see text]. Here, we show that the theory [Formula: see text] of [Formula: see text] is the model completion of the theory of STSs. We also prove that [Formula: see text] is not small and it has quantifier elimination, [Formula: see text], [Formula: see text], elimination of hyperimaginaries and weak elimination of imaginaries.<\/jats:p>","DOI":"10.1142\/s0219061320500105","type":"journal-article","created":{"date-parts":[[2019,11,12]],"date-time":"2019-11-12T08:28:41Z","timestamp":1573547321000},"page":"2050010","source":"Crossref","is-referenced-by-count":4,"title":["Model theory of Steiner triple systems"],"prefix":"10.1142","volume":"20","author":[{"given":"Silvia","family":"Barbina","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, The Open University, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Enrique","family":"Casanovas","sequence":"additional","affiliation":[{"name":"Departament de Matem\u00e0tiques i Inform\u00e0tica, Universitat de Barcelona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2019,12,31]]},"reference":[{"key":"S0219061320500105BIB001","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-41.3.557"},{"key":"S0219061320500105BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(92)00503-J"},{"key":"S0219061320500105BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(94)90148-1"},{"key":"S0219061320500105BIB005","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511623677"},{"key":"S0219061320500105BIB006","first-page":"273","volume":"54","author":"Cameron P.","year":"2012","journal-title":"Aust. 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