{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T10:16:52Z","timestamp":1773656212602,"version":"3.50.1"},"reference-count":12,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,1,15]],"date-time":"2014-01-15T00:00:00Z","timestamp":1389744000000},"content-version":"unspecified","delay-in-days":4793,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Bull. symb. log."],"published-print":{"date-parts":[[2000,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Lyndon's Interpolation Theorem asserts that for any valid implication between two purely relational sentences of first-order logic, there is an interpolant in which each relation symbol appears positively (negatively) only if it appears positively (negatively) in both the antecedent and the succedent of the given implication. We prove a similar, more general interpolation result with the additional requirement that, for some fixed tuple <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1079898600006144_inline1\"\/> of unary predicates <jats:italic>U<\/jats:italic>, all formulae under consideration have all quantifiers explicitly relativised to one of the <jats:italic>U<\/jats:italic>. Under this stipulation, existential (universal) quantification over <jats:italic>U<\/jats:italic> contributes a positive (negative) occurrence of <jats:italic>U<\/jats:italic>.<\/jats:p><jats:p>It is shown how this single new interpolation theorem, obtained by a canonical and rather elementary model theoretic proof, unifies a number of related results: the classical characterisation theorems concerning extensions (substructures) with those concerning monotonicity, as well as a many-sorted interpolation theorem focusing on positive vs. negative occurrences of predicates <jats:italic>and<\/jats:italic> on existentially vs. universally quantified sorts.<\/jats:p>","DOI":"10.2307\/420966","type":"journal-article","created":{"date-parts":[[2006,5,7]],"date-time":"2006-05-07T03:14:54Z","timestamp":1146971694000},"page":"447-462","source":"Crossref","is-referenced-by-count":16,"title":["An Interpolation Theorem"],"prefix":"10.1017","volume":"6","author":[{"given":"Martin","family":"Otto","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,1,15]]},"reference":[{"key":"S1079898600006144_ref008","first-page":"248","volume-title":"Proceedings of the international summer institute and logic colloquium, Kiel 1974","volume":"499","author":"Flum","year":"1975"},{"key":"S1079898600006144_ref004","doi-asserted-by":"publisher","DOI":"10.2307\/2963594"},{"key":"S1079898600006144_ref010","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1959.9.129"},{"key":"S1079898600006144_ref009","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511551574"},{"key":"S1079898600006144_ref007","volume-title":"JFAK. Essays dedicated to Johan van Benthem on the occasion of his 50th birthday","author":"Feferman","year":"1999"},{"key":"S1079898600006144_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0066793"},{"key":"S1079898600006144_ref005","first-page":"1","volume-title":"Proceedings of the summer school in logic, Leeds 67","volume":"70","author":"Feferman","year":"1968"},{"key":"S1079898600006144_ref012","doi-asserted-by":"publisher","DOI":"10.2307\/2272262"},{"key":"S1079898600006144_ref003","volume-title":"Model theory","author":"Chang","year":"1990"},{"key":"S1079898600006144_ref006","doi-asserted-by":"publisher","DOI":"10.1090\/pspum\/025\/0406772"},{"key":"S1079898600006144_ref011","doi-asserted-by":"publisher","DOI":"10.3792\/pja\/1195519396"},{"key":"S1079898600006144_ref002","doi-asserted-by":"publisher","DOI":"10.1093\/jigpal\/8.6.719"}],"container-title":["Bulletin of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1079898600006144","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,8]],"date-time":"2019-05-08T15:46:46Z","timestamp":1557330406000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1079898600006144\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,12]]},"references-count":12,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2000,12]]}},"alternative-id":["S1079898600006144"],"URL":"https:\/\/doi.org\/10.2307\/420966","relation":{},"ISSN":["1079-8986","1943-5894"],"issn-type":[{"value":"1079-8986","type":"print"},{"value":"1943-5894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,12]]}}}