{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T04:17:47Z","timestamp":1759033067714},"reference-count":16,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":12703,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1979,6]]},"abstract":"<jats:p>In recent years model theorists have been studying various sheaf-theoretic notions as they apply to model theory. For quite a while however, a sheaf of structures was considered to be just a local homeomorphism <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200048891_inline1\" \/> between topological spaces such that each stalk <jats:italic>S<jats:sub>x<\/jats:sub><\/jats:italic> = <jats:italic>p<\/jats:italic><jats:sup>\u22121<\/jats:sup><jats:italic>(x)<\/jats:italic> is a model-theoretic structure and such that certain maps are continuous. Some of the model-theoretic work done with this notion of a sheaf of structures are the papers by Carson [2] and Macintyre [7]. Soon came the idea of considering a sheaf of structures not just as a collection of structures glued together in some continuous way, but rather as some sort of generalized structure. A significant model-theoretic study of sheaves in this new sense became possible only after the development of the theory of topoi. As F.W. Lawvere pointed out in [6], this represents the advance of mathematics (in our case the advance of model theory) from metaphysics to dialectics.<\/jats:p><jats:p>A topos is the rather ingenious evolution of the notion of a Grothendieck topos [13]. It provides us with the idea that an object of a topos (e.g. the topos of sheaves over a topological space) may be thought of as a generalized set. Furthermore, all first-order logical operations have an interpretation in a topos, hence we may talk about generalized structures. Angus Macintyre suggested that some of his model-theoretic results about sheaves of structures may be understood better and perhaps simplified by doing model theory inside a topos of sheaves.<\/jats:p>","DOI":"10.2307\/2273725","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T21:50:09Z","timestamp":1146952209000},"page":"153-183","source":"Crossref","is-referenced-by-count":18,"title":["Sheaves and Boolean valued model theory"],"prefix":"10.1017","volume":"44","author":[{"given":"George","family":"Loullis","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200048891_ref015","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(75)90029-8"},{"key":"S0022481200048891_ref004","volume-title":"Category theory","author":"Herrlich","year":"1973"},{"key":"S0022481200048891_ref010","volume-title":"Complete theories","author":"Robinson","year":"1956"},{"key":"S0022481200048891_ref008","volume-title":"Memoirs of the American Mathematical Society","volume":"148","author":"Mulvey","year":"1974"},{"key":"S0022481200048891_ref003","volume-title":"Algebraic curves","author":"Fulton","year":"1969"},{"key":"S0022481200048891_ref013","volume-title":"Lecture Notes in Mathematics","volume":"269","year":"1972"},{"key":"S0022481200048891_ref007","doi-asserted-by":"publisher","DOI":"10.4064\/fm-81-1-73-89"},{"key":"S0022481200048891_ref012","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0080985"},{"key":"S0022481200048891_ref011","volume-title":"Introduction to model-theory and to the metamathematics of algebra","author":"Robinson","year":"1963"},{"key":"S0022481200048891_ref001","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(74)90037-1"},{"key":"S0022481200048891_ref014","unstructured":"Shorb A. M. , Contributions to Boolean-valued model theory, Ph.D. Thesis, University of Minnesota, 1969."},{"key":"S0022481200048891_ref006","volume-title":"Proceedings of the Logic Colloquium, Bristol 1973","author":"Lawvere","year":"1975"},{"key":"S0022481200048891_ref005","volume-title":"A category approach to boolean-valued set theory","author":"Higgs"},{"key":"S0022481200048891_ref009","volume-title":"Memoirs of the American Mathematical Society","author":"Pierce","year":"1967"},{"key":"S0022481200048891_ref016","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0061296"},{"key":"S0022481200048891_ref002","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(73)90169-5"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200048891","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,26]],"date-time":"2019-05-26T21:20:37Z","timestamp":1558905637000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200048891\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1979,6]]},"references-count":16,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1979,6]]}},"alternative-id":["S0022481200048891"],"URL":"https:\/\/doi.org\/10.2307\/2273725","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1979,6]]}}}