{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,1,30]],"date-time":"2024-01-30T21:10:32Z","timestamp":1706649032484},"reference-count":16,"publisher":"Duke University Press","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Notre Dame J. Formal Logic"],"published-print":{"date-parts":[[2013,1,1]]},"DOI":"10.1215\/00294527-1731335","type":"journal-article","created":{"date-parts":[[2012,12,14]],"date-time":"2012-12-14T14:15:27Z","timestamp":1355494527000},"source":"Crossref","is-referenced-by-count":2,"title":["dp-Rank and Forbidden Configurations"],"prefix":"10.1215","volume":"54","author":[{"given":"Hunter","family":"Johnson","sequence":"first","affiliation":[]}],"member":"73","reference":[{"key":"3","doi-asserted-by":"publisher","unstructured":"[3] Aschenbrenner, M., A. Dolich, D. Haskell, H. D. MacPherson, and S. Starchenko, \u201cVapnik\u2013Chervonenkis density in some theories without the independence property, I,\u201d preprint, <a href=\"arXiv:1109.5438v1\">arXiv:1109.5438v1<\/a> [math.LO]","DOI":"10.1090\/tran\/6659"},{"key":"7","doi-asserted-by":"publisher","unstructured":"[7] Guingona, V., and C. Donnay Hill, \u201cLocal dp-rank and VC-density over indiscernible sequences,\u201d preprint, <a href=\"arXiv:1108.2554v2\">arXiv:1108.2554v2<\/a> [math.LO]","DOI":"10.1002\/malq.201300040"},{"key":"8","doi-asserted-by":"publisher","unstructured":"[8] Kaplan, I., A. Onshuus, and A. Usvyatsov, \u201cAdditivity of the dp-rank,\u201d preprint, <a href=\"arXiv:1109.1601v2\">arXiv:1109.1601v2<\/a> [math.LO]","DOI":"10.1090\/S0002-9947-2013-05782-0"},{"key":"1","unstructured":"[1] Adler, H., \u201cIntroduction to theories without the independence property,\u201d to appear in <i>Archive for Mathematical Logic<\/i>."},{"key":"2","doi-asserted-by":"crossref","unstructured":"[2] Adler, H., \u201cStrong theories, burden, and weight,\u201d preprint, 2007.","DOI":"10.1126\/stke.3902007tw202"},{"key":"4","unstructured":"[4] Dudley, R. M., <i>Uniform Central Limit Theorems<\/i>, vol. 63 of <i>Cambridge Studies in Advanced Mathematics<\/i>, Cambridge University Press, Cambridge, 1999."},{"key":"5","doi-asserted-by":"crossref","unstructured":"[5] Floyd, S., \u201cSpace-bounded learning and the Vapnik\u2013Chervonenkis dimension,\u201d pp. 349\u201364 in <i>Proceedings of the Second Annual Workshop on Computational Learning Theory (Santa Cruz, Calif., 1989)<\/i>, Morgan Kaufmann, San Mateo, Calif., 1989.","DOI":"10.1016\/B978-0-08-094829-4.50028-3"},{"key":"6","doi-asserted-by":"publisher","unstructured":"[6] Guingona, V., \u201cOn uniform definability of types over finite sets,\u201d <i>Journal of Symbolic Logic<\/i>, vol. 77 (2012), 499\u2013514.","DOI":"10.2178\/jsl\/1333566634"},{"key":"9","doi-asserted-by":"crossref","unstructured":"[9] Laskowski, M. C., \u201cVapnik\u2013Chervonenkis classes of definable sets,\u201d <i>Journal of the London Mathematical Society (2)<\/i>, vol. 45 (1992), pp. 377\u201384.","DOI":"10.1112\/jlms\/s2-45.2.377"},{"key":"10","doi-asserted-by":"publisher","unstructured":"[10] Onshuus, A., and A. Usvyatsov, \u201cOn dp-minimality, strong dependence and weight,\u201d <i>Journal of Symbolic Logic<\/i>, vol. 76 (2011), pp. 737\u201358.","DOI":"10.2178\/jsl\/1309952519"},{"key":"11","doi-asserted-by":"publisher","unstructured":"[11] Sauer, N., \u201cOn the density of families of sets,\u201d <i>Journal of Combinatorial Theory (Series A)<\/i>, vol. 13 (1972), 145\u201347.","DOI":"10.1016\/0097-3165(72)90019-2"},{"key":"12","doi-asserted-by":"publisher","unstructured":"[12] Shelah, S., \u201cA combinatorial problem: Stability and order for models and theories in infinitary languages,\u201d <i>Pacific Journal of Mathematics<\/i>, vol. 41 (1972), pp. 247\u201361.","DOI":"10.2140\/pjm.1972.41.247"},{"key":"13","doi-asserted-by":"publisher","unstructured":"[13] Shelah, S., \u201cDependent first order theories, continued,\u201d <i>Israel Journal of Mathematics<\/i>, vol. 173 (2009), pp. 1\u201360.","DOI":"10.1007\/s11856-009-0082-1"},{"key":"14","doi-asserted-by":"publisher","unstructured":"[14] Shelah, S., \u201cStrongly dependent theories,\u201d to appear in <i>Israel Journal of Mathematics<\/i>.","DOI":"10.1007\/s11856-014-1111-2"},{"key":"15","doi-asserted-by":"crossref","unstructured":"[15] Vapnik, V., and A. Chervonenkis, \u201cOn the uniform convergence of relative frequencies of events to their probabilities,\u201d <i>Theory of Probability and its Applications<\/i>, vol. 16 (1971), pp. 264\u201380.","DOI":"10.1137\/1116025"},{"key":"16","unstructured":"[16] Welzl, E., \u201cComplete range spaces,\u201d unpublished notes, 1987."}],"container-title":["Notre Dame Journal of Formal Logic"],"original-title":[],"link":[{"URL":"https:\/\/projecteuclid.org\/journalArticle\/Download?urlid=10.1215\/00294527-1731335","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,30]],"date-time":"2024-01-30T20:57:59Z","timestamp":1706648279000},"score":1,"resource":{"primary":{"URL":"https:\/\/projecteuclid.org\/journals\/notre-dame-journal-of-formal-logic\/volume-54\/issue-1\/dp-Rank-and-Forbidden-Configurations\/10.1215\/00294527-1731335.full"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,1,1]]},"references-count":16,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2013,1,1]]}},"URL":"https:\/\/doi.org\/10.1215\/00294527-1731335","relation":{},"ISSN":["0029-4527"],"issn-type":[{"value":"0029-4527","type":"print"}],"subject":[],"published":{"date-parts":[[2013,1,1]]}}}