{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,1,30]],"date-time":"2024-01-30T21:10:01Z","timestamp":1706649001889},"reference-count":20,"publisher":"Duke University Press","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Notre Dame J. Formal Logic"],"published-print":{"date-parts":[[2004,10,1]]},"DOI":"10.1305\/ndjfl\/1099238447","type":"journal-article","created":{"date-parts":[[2004,11,2]],"date-time":"2004-11-02T14:23:56Z","timestamp":1099405436000},"source":"Crossref","is-referenced-by-count":1,"title":["Ultrasheaves and Double Negation"],"prefix":"10.1215","volume":"45","author":[{"given":"Steve","family":"Awodey","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jonas","family":"Eliasson","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"73","reference":[{"key":"1","doi-asserted-by":"crossref","unstructured":"[1] Blass, A., \"Two closed categories of filters\", <i>Fundamenta Mathematicae<\/i>, vol. 94 (1977), pp. 129--43.","DOI":"10.4064\/fm-94-2-129-143"},{"key":"3","unstructured":"[3] Chang, C. C., and H. J. Keisler, <i>Model Theory<\/i>, 3d edition, vol. 73 of <i>Studies in Logic and the Foundations of Mathematics<\/i>, North-Holland Publishing Co., Amsterdam, 1990."},{"key":"6","doi-asserted-by":"publisher","unstructured":"[6] Ellerman, D. P., \"Sheaves of structures and generalized ultraproducts\", <i>Annals of Mathematical Logic<\/i>, vol. 7 (1974), pp. 163--95.","DOI":"10.1016\/0003-4843(74)90014-X"},{"key":"7","unstructured":"[7] Koubek, V., and J. Reiterman, \"On the category of filters\", <i>Commentationes Mathematicae Universitatis Carolinae<\/i>, vol. 11 (1970), pp. 19--29."},{"key":"8","doi-asserted-by":"crossref","unstructured":"[8] Mac Lane, S., and I. Moerdijk, <i>Sheaves in Geometry and Logic. A First Introduction to Topos Theory<\/i>, Universitext. Springer-Verlag, New York, 1994. Corrected reprint of the 1992 edition.","DOI":"10.1007\/978-1-4612-0927-0"},{"key":"9","doi-asserted-by":"crossref","unstructured":"[9] Makkai, M., \"The topos of types\", pp. 157--201 in <i>Logic Year 1979--80 (Proceedings of Seminars and Conferences in Mathematical Logic, Storrs, 1979\/80)<\/i>, vol. 859 of <i>Lecture Notes in Mathematics<\/i>, Springer, Berlin, 1981.","DOI":"10.1007\/BFb0090947"},{"key":"10","doi-asserted-by":"publisher","unstructured":"[10] Moerdijk, I., \"A model for intuitionistic non-standard arithmetic. A tribute to Dirk van Dalen\", <i>Annals of Pure and Applied Logic<\/i>, vol. 73 (1995), pp. 37--51.","DOI":"10.1016\/0168-0072(93)E0071-U"},{"key":"11","doi-asserted-by":"crossref","unstructured":"[11] Moerdijk, I., and E. Palmgren, \"Minimal models of Heyting arithmetic\", <i>The Journal of Symbolic Logic<\/i>, vol. 62 (1997), pp. 1448--60.","DOI":"10.2307\/2275651"},{"key":"12","doi-asserted-by":"publisher","unstructured":"[12] Nelson, E., \"Internal set theory: A new approach to nonstandard analysis\", <i>Bulletin of the American Mathematical Society<\/i>, vol. 83 (1977), pp. 1165--98.","DOI":"10.1090\/S0002-9904-1977-14398-X"},{"key":"13","doi-asserted-by":"publisher","unstructured":"[13] Palmgren, E., \"A sheaf-theoretic foundation for nonstandard analysis\", <i>Annals of Pure and Applied Logic<\/i>, vol. 85 (1997), pp. 69--86.","DOI":"10.1016\/S0168-0072(96)00041-3"},{"key":"14","doi-asserted-by":"crossref","unstructured":"[14] Palmgren, E., \"Developments in constructive nonstandard analysis\", <i>The Bulletin of Symbolic Logic<\/i>, vol. 4 (1998), pp. 233--72.","DOI":"10.2307\/421031"},{"key":"15","doi-asserted-by":"publisher","unstructured":"[15] Palmgren, E., \"Real numbers in the topos of sheaves over the category of filters\", <i>Journal of Pure and Applied Algebra<\/i>, vol. 160 (2001), pp. 275--84.","DOI":"10.1016\/S0022-4049(00)00080-3"},{"key":"16","doi-asserted-by":"crossref","unstructured":"[16] Palmgren, E., \"Unifying constructive and nonstandard analysis\", pp. 167--83 in <i>Reuniting the Antipodes---Constructive and Nonstandard Views of the Continuum (Venice, 1999)<\/i>, vol. 306 of <i>Synthese Library<\/i>, Kluwer Academic Publishers, Dordrecht, 2001.","DOI":"10.1007\/978-94-015-9757-9_15"},{"key":"17","doi-asserted-by":"publisher","unstructured":"[17] Pitts, A. M., \"Amalgamation and interpolation in the category of Heyting algebras\", <i>Journal of Pure and Applied Algebra<\/i>, vol. 29 (1983), pp. 155--65.","DOI":"10.1016\/0022-4049(83)90104-4"},{"key":"18","doi-asserted-by":"publisher","unstructured":"[18] Pitts, A. M., \"An application of open maps to categorical logic\", <i>Journal of Pure and Applied Algebra<\/i>, vol. 29 (1983), pp. 313--26.","DOI":"10.1016\/0022-4049(83)90047-6"},{"key":"19","doi-asserted-by":"publisher","unstructured":"[19] Pitts, A. M., \"Conceptual completeness for first-order intuitionistic logic: An application of categorical logic\", <i>Annals of Pure and Applied Logic<\/i>, vol. 41 (1989), pp. 33--81.","DOI":"10.1016\/0168-0072(89)90007-9"},{"key":"20","unstructured":"[20] Troelstra, A. S., and D. van Dalen, <i>Constructivism in Mathematics. An Introduction. Vol. I<\/i>, vol. 121 of <i>Studies in Logic and the Foundations of Mathematics<\/i>, North-Holland Publishing Co., Amsterdam, 1988."},{"key":"2","unstructured":"[2] Butz, C., \"Saturated Models of Intuitionistic Theories\", unpublished manuscript."},{"key":"4","doi-asserted-by":"publisher","unstructured":"[4] Eliasson, J., \"Ultrapowers as sheaves on a category of ultrafilters\", <i>Archive for Mathematical Logic<\/i>, vol. 43 (2004), pp. 825--843.","DOI":"10.1007\/s00153-004-0228-0"},{"key":"5","unstructured":"[5] Eliasson, J., \"Ultrasheaves and Ultrapowers\", in preparation."}],"container-title":["Notre Dame Journal of Formal Logic"],"original-title":[],"link":[{"URL":"https:\/\/projecteuclid.org\/journalArticle\/Download?urlid=10.1305\/ndjfl\/1099238447","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,30]],"date-time":"2024-01-30T20:56:11Z","timestamp":1706648171000},"score":1,"resource":{"primary":{"URL":"https:\/\/projecteuclid.org\/journals\/notre-dame-journal-of-formal-logic\/volume-45\/issue-4\/Ultrasheaves-and-Double-Negation\/10.1305\/ndjfl\/1099238447.full"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,10,1]]},"references-count":20,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2004,10,1]]}},"URL":"https:\/\/doi.org\/10.1305\/ndjfl\/1099238447","relation":{},"ISSN":["0029-4527"],"issn-type":[{"value":"0029-4527","type":"print"}],"subject":[],"published":{"date-parts":[[2004,10,1]]}}}