Semi-bounded relations in ordered modules
| dc.contributor.author | Belegradek, O | |
| dc.date.accessioned | 2024-07-18T20:49:11Z | |
| dc.date.available | 2024-07-18T20:49:11Z | |
| dc.date.issued | 2004 | |
| dc.department | İstanbul Bilgi Üniversitesi | en_US |
| dc.description.abstract | A relation on a linearly ordered structure is called semi-bounded if it is definable in an expansion of the structure by bounded relations. We study ultimate behavior of semi-bounded relations in an ordered module M over an ordered commutative ring R such that M/rM is finite for all nonzero r is an element of R. We consider M as a structure in the language of ordered R-modules augmented by relation symbols for the submodules rM, and prove several quantifier elimination results for semi-bounded relations and functions in M. We show that these quantifier elimination results essentially characterize the ordered modules M with finite indices of the submodules rM. It is proven that (1) any semi-bounded k-ary relation on M is equal, outside a finite union of k-strips, to a k-ary relation quantifier-free definable in M, (2) any semi-bounded function from M-k to M is equal, outside a finite union of k-strips, to a piecewise linear function, and (3) any semi-bounded in M endomorphism of the additive group of M is of the form x --> sigmax, for some sigma from the field of fractions of R. | en_US |
| dc.identifier.doi | 10.2178/jsl/1082418540 | |
| dc.identifier.endpage | 517 | en_US |
| dc.identifier.issn | 0022-4812 | |
| dc.identifier.issn | 1943-5886 | |
| dc.identifier.issue | 2 | en_US |
| dc.identifier.scopus | 2-s2.0-2942690008 | en_US |
| dc.identifier.scopusquality | Q1 | en_US |
| dc.identifier.startpage | 499 | en_US |
| dc.identifier.uri | https://doi.org/10.2178/jsl/1082418540 | |
| dc.identifier.uri | https://hdl.handle.net/11411/8121 | |
| dc.identifier.volume | 69 | en_US |
| dc.identifier.wos | WOS:000221710700012 | 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 | Cambridge Univ Press | en_US |
| dc.relation.ispartof | Journal of Symbolic Logic | en_US |
| dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
| dc.rights | info:eu-repo/semantics/closedAccess | en_US |
| dc.title | Semi-bounded relations in ordered modules | |
| dc.type | Article |
