On the additive group structure of the nonstandard models of the theory of integers
| dc.contributor.author | Dalgin, H | |
| dc.contributor.author | Haddad, L | |
| dc.contributor.author | Terziler, M | |
| dc.date.accessioned | 2019-10-27T18:18:43Z | |
| dc.date.available | 2019-10-27T18:18:43Z | |
| dc.date.issued | 2002 | |
| dc.department | Ege Üniversitesi | en_US |
| dc.description.abstract | Let (Z) over cap (+) denote the inverse limit of all finite cyclic groups. Let F, G and H be abelian groups with H less than or equal to G. Let FbetaH denote the abelian group (F x H, +(beta)), where +(beta) is defined by (alpha, x) +(beta) (b, y) = (a + b, x + y + beta(a) + beta(b) - beta(a + b)) for a certain beta : F --> G linear mod H meaning that beta(0) = 0 and beta(a) + beta(b) - beta(a + b) epsilon H for all a, b in F. In this paper we show that the following hold: (1) The additive group of any nonstandard model Z* of the ring Z is isomorphic to (Z(+)*/H)betaH for a certain beta:Z(+)*/H --> (Z) over cap (+) linear mod H. (2) (Z) over cap (+) is isomorphic to ((Z) over cap (+)/H)betaH for some beta:(Z) over cap (+)/H --> Q linear mod H, though (Z) over cap (+) is not the additive group of any model of Th(Z,+, x) and the exact sequence H --> (Z) over cap (+) --> (Z) over cap (+)/H is not splitting. | en_US |
| dc.identifier.doi | 10.1002/1521-3870(200204)48:3<403 | |
| dc.identifier.endpage | 412 | en_US |
| dc.identifier.issn | 0942-5616 | |
| dc.identifier.issn | 0942-5616 | en_US |
| dc.identifier.issue | 3 | en_US |
| dc.identifier.scopusquality | N/A | en_US |
| dc.identifier.startpage | 403 | en_US |
| dc.identifier.uri | https://doi.org/10.1002/1521-3870(200204)48:3<403 | |
| dc.identifier.uri | https://hdl.handle.net/11454/35534 | |
| dc.identifier.volume | 48 | en_US |
| dc.identifier.wos | WOS:000175167200009 | en_US |
| dc.identifier.wosquality | Q3 | en_US |
| dc.indekslendigikaynak | Web of Science | en_US |
| dc.indekslendigikaynak | Scopus | en_US |
| dc.language.iso | en | en_US |
| dc.publisher | Wiley-V C H Verlag Gmbh | en_US |
| dc.relation.ispartof | Mathematical Logic Quarterly | en_US |
| dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
| dc.rights | info:eu-repo/semantics/closedAccess | en_US |
| dc.subject | nonstandard model of arithmetic | en_US |
| dc.subject | linear mod 1 function | en_US |
| dc.subject | fiber product | en_US |
| dc.title | On the additive group structure of the nonstandard models of the theory of integers | en_US |
| dc.type | Article | en_US |
