{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,2,14]],"date-time":"2024-02-14T15:42:40Z","timestamp":1707925360853},"reference-count":19,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,11,13]],"date-time":"2006-11-13T00:00:00Z","timestamp":1163376000000},"content-version":"vor","delay-in-days":3969,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1996,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Every model of I\u0394<jats:sub>0<\/jats:sub>is the tally part of a model of the stringlanguage theory Th\u2010FO (a main feature of which consists in having induction on notation restricted to certain<jats:italic>AC<\/jats:italic><jats:sup>0<\/jats:sup>. sets). We show how to \u201csmoothly\u201d introduce in Th\u2010FO the binary length function, whereby it is possible to make exponential assumptions in models of Th\u2010FO. These considerations entail that every model of I\u0394<jats:sub>0<\/jats:sub>+ \u00acexp is a proper initial segment of a model of Th\u2010FO and that a<jats:italic>modicum<\/jats:italic>of bounded collection is true in these models.<\/jats:p><jats:p>Mathematics Subject Classification: 03F30, 03C62, 68Q15.<\/jats:p>","DOI":"10.1002\/malq.19960420102","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T17:53:09Z","timestamp":1180201989000},"page":"1-18","source":"Crossref","is-referenced-by-count":3,"title":["On End\u2010Extensions of Models of \u00acexp"],"prefix":"10.1002","volume":"42","author":[{"given":"Fernando","family":"Ferreira","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,11,13]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(83)90038-6"},{"key":"e_1_2_1_3_2","unstructured":"Buss S. R. Bounded Arithmetic. Ph. D. Dissertation Princeton University 1985. A revision of this thesis was published by Bibliopolis in 1986."},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-2566-9_6"},{"key":"e_1_2_1_5_2","unstructured":"Ferreira F. Polynomial Time Computable Arithmetic and Conservative Extensions. Ph. D. Dissertation Pennsylvania State University 1988."},{"key":"e_1_2_1_6_2","unstructured":"Ferreira F. On End Extensions of Models of \u03b1exp. Preprint CMAF 22\/91 Lisboa1991."},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01270627"},{"key":"e_1_2_1_8_2","unstructured":"Ferreira F. Some notes on subword quantification and induction thereof. To appear in:Logic and Algebra in Memory of Roberto Megari."},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-22156-3"},{"key":"e_1_2_1_10_2","unstructured":"H\u00e5stad J. Computational Limitations for Small Depth Circuits. Ph. D. Dissertation Massachussetts Institute of Technology 1986."},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1090\/psapm\/038\/1020810"},{"key":"e_1_2_1_12_2","volume-title":"Oxford Logic Guides 15","author":"Kaye R.","year":"1991"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(90)90023-U"},{"key":"e_1_2_1_14_2","first-page":"199","volume-title":"Logic Coloquium 1977, Studies in Logic and the Foundations of Mathematics","author":"Paris J. B.","year":"1978"},{"key":"e_1_2_1_15_2","series-title":"Oxford Logic Guides 23","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1093\/oso\/9780198536901.003.0012","volume-title":"Arithmetic, Proof Theory, and Computational Complexity","author":"Razborov A.","year":"1993"},{"key":"e_1_2_1_16_2","series-title":"Oxford Logic Guides 23","doi-asserted-by":"crossref","first-page":"364","DOI":"10.1093\/oso\/9780198536901.003.0016","volume-title":"Arithmetic, Proof Theory, and Computational Complexity","author":"Takeuti G.","year":"1993"},{"key":"e_1_2_1_17_2","first-page":"5","volume-title":"Mod\u00e8les non standard en arithm\u00e9tique et th\u00e9orie des ensembles","author":"Wilkie A. J.","year":"1987"},{"key":"e_1_2_1_18_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(08)70042-9"},{"key":"e_1_2_1_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(87)90066-2"},{"key":"e_1_2_1_20_2","unstructured":"Zambella D. Chapters in Bounded Arithmetic and Provability Logic. Ph. D. Dissertation Universiteit van Amsterdam 1994."}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19960420102","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19960420102","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,14]],"date-time":"2024-02-14T15:27:44Z","timestamp":1707924464000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19960420102"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,1]]},"references-count":19,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1996,1]]}},"alternative-id":["10.1002\/malq.19960420102"],"URL":"https:\/\/doi.org\/10.1002\/malq.19960420102","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,1]]}}}