{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T11:20:31Z","timestamp":1772450431172,"version":"3.50.1"},"reference-count":21,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,1,15]],"date-time":"2014-01-15T00:00:00Z","timestamp":1389744000000},"content-version":"unspecified","delay-in-days":501,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Bull. symb. log"],"published-print":{"date-parts":[[2012,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In his 1967 paper Vaught used an ingenious argument to show that every recursively enumerable first order theory that directly interprets the weak system VS of set theory is axiomatizable by a scheme. In this paper we establish a strengthening of Vaught's theorem by weakening the hypothesis of direct interpretability of VS to direct interpretability of the finitely axiomatized fragment VS<jats:sub>2<\/jats:sub>of VS. This improvement significantly increases the scope of the original result, since VS is essentially undecidable, but VS<jats:sub>2<\/jats:sub>has decidable extensions. We also explore the ramifications of our work on finite axiomatizability of schemes in the presence of suitable comprehension principles.<\/jats:p>","DOI":"10.2178\/bsl\/1344861888","type":"journal-article","created":{"date-parts":[[2012,8,13]],"date-time":"2012-08-13T12:44:52Z","timestamp":1344861892000},"page":"382-402","source":"Crossref","is-referenced-by-count":7,"title":["Vaught's Theorem on Axiomatizability by a Scheme"],"prefix":"10.1017","volume":"18","author":[{"given":"Albert","family":"Visser","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,1,15]]},"reference":[{"key":"S1079898600000032_ref014","volume-title":"Undecidable theories","author":"Tarski","year":"1953"},{"key":"S1079898600000032_ref002","first-page":"219","volume":"12","author":"Corcoran","year":"2006","journal-title":"Schemata: the concept of schema in the history of logic"},{"key":"S1079898600000032_ref021","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(87)90066-2"},{"key":"S1079898600000032_ref010","volume-title":"A lattice of chapters of mathematics (Interpretations between theorems","volume":"426","author":"Mycielski","year":"1990"},{"key":"S1079898600000032_ref009","volume-title":"Aspects of Incompleteness","volume":"10","author":"Lindstr\u00f6m","year":"2002"},{"key":"S1079898600000032_ref017","first-page":"284","volume-title":"Logic in Tehran. 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