{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T17:47:16Z","timestamp":1648748836319},"reference-count":20,"publisher":"Elsevier BV","issue":"1-2","license":[{"start":{"date-parts":[[2001,4,1]],"date-time":"2001-04-01T00:00:00Z","timestamp":986083200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2013,7,17]],"date-time":"2013-07-17T00:00:00Z","timestamp":1374019200000},"content-version":"vor","delay-in-days":4490,"URL":"https:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Theoretical Computer Science"],"published-print":{"date-parts":[[2001,4]]},"DOI":"10.1016\/s0304-3975(00)00106-7","type":"journal-article","created":{"date-parts":[[2002,7,25]],"date-time":"2002-07-25T10:59:17Z","timestamp":1027594757000},"page":"1-15","source":"Crossref","is-referenced-by-count":0,"title":["Weak Arithmetics"],"prefix":"10.1016","volume":"257","author":[{"given":"J.-P.","family":"Ressayre","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/S0304-3975(00)00106-7_BIB1","doi-asserted-by":"crossref","unstructured":"P. d'Aquino, A. Macintyre, Non standard finite fields over I\u03940 + \u03a91, Israel J. Math., 1999, to appear.","DOI":"10.1007\/BF02773575"},{"key":"10.1016\/S0304-3975(00)00106-7_BIB2","unstructured":"S. Buss, Bounded Arithmetic, Bibliopolis, 1986."},{"key":"10.1016\/S0304-3975(00)00106-7_BIB3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1090\/S0273-0979-1989-15750-9","article-title":"On a theory of computation and complexity over the real numbers","volume":"21","author":"Blum","year":"1989","journal-title":"Bull. Am. Math. Soc."},{"key":"10.1016\/S0304-3975(00)00106-7_BIB4","unstructured":"S. Boughattas, Trois theoremes sur l'induction ouverte munie de l'exponentielle, J. Symbolic Log, 1991, to appear."},{"key":"10.1016\/S0304-3975(00)00106-7_BIB5","unstructured":"P. Cegielski, Le theoreme de Dirichlet est finitiste, Prepublications du LITP, 1992."},{"key":"10.1016\/S0304-3975(00)00106-7_BIB6","unstructured":"O. Chapuis, P. Koiran, Saturation and stability in the theory of computation over the reals, Prepublications de l'Institut Girard Desargues, 1997."},{"key":"10.1016\/S0304-3975(00)00106-7_BIB7","series-title":"Tame topology and o-minimal structures","volume":"Vol. 248","author":"van den Dries","year":"1999"},{"key":"10.1016\/S0304-3975(00)00106-7_BIB8","unstructured":"J. Duparc, O. Finkel, J.P. Ressayre, Computer Science and the fine structure of Borel sets, Theoret. Comput. Sci., 1999, this volume."},{"key":"10.1016\/S0304-3975(00)00106-7_BIB9","unstructured":"J. van der Hoeven, Asymptotique automatique, These Universite de Paris 7, 1997."},{"key":"10.1016\/S0304-3975(00)00106-7_BIB10","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1215\/S0012-7094-42-00922-0","article-title":"Maximal fields with valuations","volume":"9","author":"Kaplansky","year":"1942","journal-title":"Duke Math. J."},{"key":"10.1016\/S0304-3975(00)00106-7_BIB11","doi-asserted-by":"crossref","unstructured":"R. Kaye, Diophantine induction Anal. Pure Appl. Logic (46) 1990.","DOI":"10.1016\/0168-0072(90)90076-E"},{"key":"10.1016\/S0304-3975(00)00106-7_BIB12","series-title":"Bounded Arithmetic, Propositional Logic and Complexity Theory","author":"Krajicek","year":"1995"},{"key":"10.1016\/S0304-3975(00)00106-7_BIB13","unstructured":"J. Krajicek, Uniform families of polynomial equations over finite fields and first order structures with Euler characteristic, preprint, 1998."},{"key":"10.1016\/S0304-3975(00)00106-7_BIB14","series-title":"Les Petits Cailloux","author":"Poizat","year":"1995"},{"key":"10.1016\/S0304-3975(00)00106-7_BIB15","unstructured":"N. Portier, Stabilite polynomiale des corps differentiels, Prepublications de l'Institut Girard Desargues, 1997."},{"key":"10.1016\/S0304-3975(00)00106-7_BIB16","unstructured":"J.P. Ressayre, Polynomial time uniformization for open exponential induction, preprint, 1995."},{"key":"10.1016\/S0304-3975(00)00106-7_BIB17","doi-asserted-by":"crossref","unstructured":"J.P. Ressayre, 1996 La th\u00e9orie des mod\u00e8les et un petit probl\u00e8me de Hardy, Development of Mathematics 2000, Birkh\u00e4user, Basel, 1996, to appear.","DOI":"10.1007\/978-3-0348-8968-1_31"},{"key":"10.1016\/S0304-3975(00)00106-7_BIB18","unstructured":"O. Sudac, Le theoreme de repartition des nombres premiers se demontre dans PRA, Theoret. Comput. Sci., 1998, this volume."},{"key":"10.1016\/S0304-3975(00)00106-7_BIB19","series-title":"Two applications of Logic to Mathematics","author":"Takeuti","year":"1978"},{"key":"10.1016\/S0304-3975(00)00106-7_BIB20","doi-asserted-by":"crossref","first-page":"1051","DOI":"10.1090\/S0894-0347-96-00216-0","article-title":"Model completeness results for expansions of the ordered field of real numbers by restricted pfaffian functions and the exponential function","volume":"9","author":"Wilkie","year":"1996","journal-title":"J. Amer. Math. Soc."}],"container-title":["Theoretical Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0304397500001067?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0304397500001067?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2020,1,8]],"date-time":"2020-01-08T04:48:28Z","timestamp":1578458908000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0304397500001067"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,4]]},"references-count":20,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2001,4]]}},"alternative-id":["S0304397500001067"],"URL":"https:\/\/doi.org\/10.1016\/s0304-3975(00)00106-7","relation":{},"ISSN":["0304-3975"],"issn-type":[{"value":"0304-3975","type":"print"}],"subject":[],"published":{"date-parts":[[2001,4]]}}}