{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,11,17]],"date-time":"2023-11-17T04:10:36Z","timestamp":1700194236230},"reference-count":11,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2004,2,3]],"date-time":"2004-02-03T00:00:00Z","timestamp":1075766400000},"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":[[2004,3]]},"abstract":"Abstract<\/jats:title>We prove that the finite\u2010model version of arithmetic with the divisibility relation is undecidable (more precisely, it has \u03a00<\/jats:sup>1<\/jats:sub>\u2010complete set of theorems). Additionally we prove FM\u2010representability theorem for this class of finite models. This means that a relation R<\/jats:italic> on natural numbers can be described correctly on each input on almost all finite divisibility models if and only if R<\/jats:italic> is of degree \u22640<\/jats:bold>\u2032. We obtain these results by interpreting addition and multiplication on initial segments of finite models with divisibility only. (\u00a9 2004 WILEY\u2010VCH Verlag GmbH & Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200310086","type":"journal-article","created":{"date-parts":[[2004,2,4]],"date-time":"2004-02-04T13:02:17Z","timestamp":1075899737000},"page":"169-174","source":"Crossref","is-referenced-by-count":5,"title":["Arithmetic of divisibility in finite models"],"prefix":"10.1002","volume":"50","author":[{"given":"Marcin","family":"Mostowski","sequence":"first","affiliation":[]},{"given":"Anna E.","family":"Wasilewska","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2004,2,3]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"L.Ko\u0142odziejczyk Truth definitions in finite models. J. Symbolic Logic (in printing)."},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(00)00113-4"},{"key":"e_1_2_1_4_2","unstructured":"M.Krynicki andK.Zdanowski Theories of arithmetics in finite models. J. Symbolic Logic (to appear)."},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.200310041"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1002\/1521-3870(200111)47:4<513::AID-MALQ513>3.0.CO;2-J"},{"key":"e_1_2_1_7_2","doi-asserted-by":"crossref","unstructured":"M.Mostowski On representing semantics in finite models. In: Philosophical Dimensions of Logic and Science (A. Rojszczak J. Cachro and G. Kurczewski eds.) pp. 15\u201328 (Kluwer Acad. Publ. Amsterdam 2003).","DOI":"10.1007\/978-94-017-2612-2_2"},{"key":"e_1_2_1_8_2","unstructured":"M.Mostowski andK.Zdanowski Beyond FM\u2010representability. In preparation."},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.2307\/2266510"},{"key":"e_1_2_1_10_2","unstructured":"W.Sierpi\u0144ski Elementary Theory of Numbers (PWN \u2013 Polish Scientific Publishers Warszawa 1964)."},{"key":"e_1_2_1_11_2","doi-asserted-by":"crossref","unstructured":"J. R.Shoenfield Recursion Theory (Springer\u2010Verlag Berlin et al. 1993).","DOI":"10.1007\/978-3-662-22378-9"},{"key":"e_1_2_1_12_2","unstructured":"K.Zdanowski Arithmetics in finite but potentially infinite worlds. Ph. D. Thesis Warsaw University (in preparation)."}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.200310086","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.200310086","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,17]],"date-time":"2023-11-17T03:29:36Z","timestamp":1700191776000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.200310086"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,2,3]]},"references-count":11,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2004,3]]}},"alternative-id":["10.1002\/malq.200310086"],"URL":"https:\/\/doi.org\/10.1002\/malq.200310086","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,2,3]]}}}