{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,1,8]],"date-time":"2025-01-08T23:10:11Z","timestamp":1736377811379,"version":"3.32.0"},"reference-count":13,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2006,5,11]],"date-time":"2006-05-11T00:00:00Z","timestamp":1147305600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2006,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Suppose that it is possible to integrate real functions over a weak base theory related to polynomial time computability. Does it follow that we can count? The answer seems to be: obviously yes! We try to convince the reader that the severe restrictions on induction in feasible theories preclude a straightforward answer. Nevertheless, a more sophisticated reflection does indeed show that the answer is affirmative. (\u00a9 2006 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200510035","type":"journal-article","created":{"date-parts":[[2006,5,11]],"date-time":"2006-05-11T11:58:35Z","timestamp":1147348715000},"page":"315-320","source":"Crossref","is-referenced-by-count":0,"title":["Counting as integration in feasible analysis"],"prefix":"10.1002","volume":"52","author":[{"given":"Fernando","family":"Ferreira","sequence":"first","affiliation":[]},{"given":"Gilda","family":"Ferreira","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,5,11]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"S.Buss Bounded arithmetic. Ph.D. thesis Princeton University New Jersey 1985. A revision of this thesis was published by Bibliopolis (Naples) in 1986."},{"key":"e_1_2_1_3_2","unstructured":"F.Ferreira Polynomial time computable arithmetic and conservative extensions. Ph.D. thesis Pennsylvania State University Pennsylvania 1988."},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.2307\/2275924"},{"key":"e_1_2_1_5_2","unstructured":"G.Ferreira Sistemas de an\u00e1lise fraca para a integra\u00e7\u00e3o. Ph. D. thesis (in Portuguese) Universidade de Lisboa Portugal. Forthcoming."},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1190150098"},{"key":"e_1_2_1_7_2","doi-asserted-by":"crossref","unstructured":"P.H\u00e1jek andP.Pudl\u00e1k Metamathematics of First\u2010Order Arithmetic. Perspectives in Mathematical Logic (Springer 1993).","DOI":"10.1007\/978-3-662-22156-3"},{"key":"e_1_2_1_8_2","doi-asserted-by":"crossref","unstructured":"J.Johannsen andC.Pollett On proofs about threshold circuits and counting hierarchies (extended abstract). In: Thirteenth Annual IEEE Symposium on Logic in Computer Science pp. 444\u2013452 (IEEE Press 1998).","DOI":"10.1109\/LICS.1998.705678"},{"key":"e_1_2_1_9_2","unstructured":"K.\u2010I.Ko Complexity Theory of Real Functions (Birkh\u00e4user 1991)."},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(82)80003-0"},{"key":"e_1_2_1_11_2","doi-asserted-by":"crossref","unstructured":"J.Kraj\u00ed\u010dek Bounded Arithmetic Propositional Logic and Complexity Theory. Encyclopedia of Mathematics and Its Applications 60 (Cambridge University Press 1995).","DOI":"10.1017\/CBO9780511529948"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.2307\/2274507"},{"key":"e_1_2_1_13_2","doi-asserted-by":"crossref","unstructured":"S.Simpson Subsystems of Second Order Arithmetic. Perspectives in Mathematical Logic (Springer 1999).","DOI":"10.1007\/978-3-642-59971-2"},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(86)90141-6"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.200510035","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.200510035","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,8]],"date-time":"2025-01-08T22:29:48Z","timestamp":1736375388000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.200510035"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,5,11]]},"references-count":13,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2006,6]]}},"alternative-id":["10.1002\/malq.200510035"],"URL":"https:\/\/doi.org\/10.1002\/malq.200510035","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"type":"print","value":"0942-5616"},{"type":"electronic","value":"1521-3870"}],"subject":[],"published":{"date-parts":[[2006,5,11]]}}}