{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,1,30]],"date-time":"2024-01-30T21:40:02Z","timestamp":1706650802284},"reference-count":16,"publisher":"Duke University Press","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Notre Dame J. Formal Logic"],"published-print":{"date-parts":[[1995,10,1]]},"DOI":"10.1305\/ndjfl\/1040136914","type":"journal-article","created":{"date-parts":[[2003,2,25]],"date-time":"2003-02-25T21:21:21Z","timestamp":1046208081000},"source":"Crossref","is-referenced-by-count":12,"title":["Arithmetically Saturated Models of Arithmetic"],"prefix":"10.1215","volume":"36","author":[{"given":"Roman","family":"Kossak","sequence":"first","affiliation":[]},{"given":"James H.","family":"Schmerl","sequence":"additional","affiliation":[]}],"member":"73","reference":[{"key":"9","unstructured":"Kossak, R., and J. Schmerl, \u201cThe automorphism group of an arithmetically saturated model of Peano arithmetic,\u201d forthcoming in <i>Journal of the London Mathematical Society<\/i>. Zbl 0905.03024 MR 97a:03048"},{"key":"3","doi-asserted-by":"publisher","unstructured":"Kaye, R., R. Kossak and H. Kotlarski, \u201cAutomorphisms of recursively saturated models of arithmetic,\u201d <i>Annals of Pure and Applied Logic<\/i>, vol. 55 (1991), pp. 67\u201399. Zbl 0748.03023 MR 93c:03047","DOI":"10.1016\/0168-0072(91)90098-7"},{"key":"1","doi-asserted-by":"publisher","unstructured":"Hodges, W., I. Hodkinson, D. Lascar and S. Shelah, \u201cThe small index property for $\\omega$-stable $\\omega$-categorical structures and for the random graph,\u201d <i>Journal of the London Mathematical Society<\/i>, vol. 48 (1993), pp. 204\u2013218. Zbl 0788.03039 MR 94d:03063","DOI":"10.1112\/jlms\/s2-48.2.204"},{"key":"2","unstructured":"Kaye, R., <i>Models of Peano Arithmetic<\/i>, Oxford Logic Guides vol. 15, Oxford University Press, Oxford, 1991. Zbl 0744.03037 MR 92k:03034"},{"key":"4","doi-asserted-by":"crossref","unstructured":"Kirby, L. A. S., <i>Initial Segments of Models of Arithmetic<\/i>, Ph.D. thesis, University of Manchester, 1977.","DOI":"10.1007\/BFb0067653"},{"key":"5","doi-asserted-by":"crossref","unstructured":"Kirby, L., \u201cUltrafilters and types of models of arithmetic,\u201d <i>Annals of Pure and Applied Logic<\/i>, vol. 27 (1984), pp. 215\u2013252. Zbl 0565.03014 MR 86f:03107","DOI":"10.1016\/0168-0072(84)90027-7"},{"key":"6","doi-asserted-by":"crossref","unstructured":"Kossak, R., \u201cModels with the $\\omega$-property,\u201d <i>The Journal of Symbolic Logic<\/i>, vol. 54 (1989), pp. 177\u2013189. Zbl 0669.03039 MR 90a:03053","DOI":"10.2307\/2275023"},{"key":"7","unstructured":"Kossak, R., \u201cExcercises in `back-and-forth',\u201d <i>Proceedings of the 9th Easter Conference in Model Theory<\/i>, edited by H. Wolter, Seminarbericht 112, Humboldt Universit\u00e4t zu Berlin, 1991. Zbl 0753.03014"},{"key":"8","doi-asserted-by":"crossref","unstructured":"Kossak, R., H. Kotlarski and J. Schmerl \u201cOn maximal subgroups of the automorphism group of a countable \\rs model of PA,\u201d <i>Annals of Pure and Applied Logic<\/i>, vol. 63 (1993), pp. 125\u2013148. Zbl 0796.03043 MR 94m:03061","DOI":"10.1016\/0168-0072(93)90035-C"},{"key":"10","doi-asserted-by":"crossref","unstructured":"Kotlarski, H., \u201cOn elementary cuts in \\rs models of Peano Arithmetic,\u201d <i>Fundamenta Mathematic\u00e6<\/i>, vol. 120 (1984), pp. 205\u2013222. Zbl 0572.03016 MR 86f:03056","DOI":"10.4064\/fm-120-3-205-222"},{"key":"11","doi-asserted-by":"crossref","unstructured":"Lascar, D., \u201cThe small index property and \\rs models of Peano arithmetic,\u201d pp. 281\u2013292 in <i>Automorphism of First Order Structures<\/i>, edited by R. Kaye and D. Macpherson, Oxford University Press Oxford, 1994. Zbl 0824.03014 MR 1325479","DOI":"10.1093\/oso\/9780198534686.003.0013"},{"key":"12","doi-asserted-by":"crossref","unstructured":"MacPherson, H. D., and P. M. Neuman, \u201cSubgroups of infinite symmetric groups,\u201d <i>Journal of the London Mathematical Society<\/i> vol. 42 (1990), pp. 64\u201384. Zbl 0668.20005 MR 92d:20006","DOI":"10.1112\/jlms\/s2-42.1.64"},{"key":"13","doi-asserted-by":"crossref","unstructured":"Schmerl, J. H., \u201cSubstructure lattices of models of Peano Arithmetic,\u201d pp. 225\u2013243 in <i>Logic Colloquium '84<\/i>, North-Holland, Amsterdam, 1986. Zbl 0596.03066 MR 87j:03046","DOI":"10.1016\/S0049-237X(08)70465-8"},{"key":"14","doi-asserted-by":"crossref","unstructured":"Schmerl, J. H., \u201cFinite substructure lattices of models of Peano Arithmetic,\u201d <i>Proceedings of the American Mathematical Society<\/i>, vol. 117 (1993), pp. 833\u2013838. Zbl 0788.03050 MR 93d:03073","DOI":"10.1090\/S0002-9939-1993-1112501-8"},{"key":"15","unstructured":"Smory\u0144ski, C., \u201cRecursively saturated non-standard models of arithmetic,\u201d <i>The Journal of Symbolic Logic<\/i>, vol. 46 (1981), pp. 329\u2013344. Zbl 0549.03059 MR 84b:03054"},{"key":"16","doi-asserted-by":"crossref","unstructured":"Wilmers, G., \u201cMinimally saturated models,\u201d pp. 370\u2013380 in <i>Model Theory of Algebra and Arithmetic<\/i>, edited by L. Pacholski et al., Lecture Notes in Mathematics vol. 834, Springer-Verlag, Berlin, 1980. Zbl 0463.03017 MR 82d:03051","DOI":"10.1007\/BFb0090175"}],"container-title":["Notre Dame Journal of Formal Logic"],"original-title":[],"link":[{"URL":"https:\/\/projecteuclid.org\/journalArticle\/Download?urlid=10.1305\/ndjfl\/1040136914","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,30]],"date-time":"2024-01-30T21:12:38Z","timestamp":1706649158000},"score":1,"resource":{"primary":{"URL":"https:\/\/projecteuclid.org\/journals\/notre-dame-journal-of-formal-logic\/volume-36\/issue-4\/Arithmetically-Saturated-Models-of-Arithmetic\/10.1305\/ndjfl\/1040136914.full"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,10,1]]},"references-count":16,"journal-issue":{"issue":"4","published-online":{"date-parts":[[1995,10,1]]}},"URL":"https:\/\/doi.org\/10.1305\/ndjfl\/1040136914","relation":{},"ISSN":["0029-4527"],"issn-type":[{"value":"0029-4527","type":"print"}],"subject":[],"published":{"date-parts":[[1995,10,1]]}}}