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The valuation difference rank of an ordered difference field

hal.structure.identifierFaculty of Mathematics and Computer Science [Konstanz]
dc.contributor.authorKUHLMANN, Salma
hal.structure.identifierFonds de la Recherche Scientifique [FNRS]
dc.contributor.authorPOINT, Francoise
hal.structure.identifierÉquipe Géométrie
dc.contributor.authorMATUSINSKI, Mickael
dc.date.accessioned2024-04-04T02:19:37Z
dc.date.available2024-04-04T02:19:37Z
dc.date.created2013-01-11
dc.date.issued2017-11-01
dc.identifier.isbn978-3-319-51717-9
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/189419
dc.description.abstractEnThere are several equivalent characterizations of the valuation rank of an ordered field (endowed with its natural valuation). In this paper, we extend the theory to the case of an ordered difference field and introduce the notion of {\it difference rank}. We characterize the difference rank as the quotient modulo the equivalence relation naturally induced by the automorphism (which encodes its growth rate). In analogy to the theory of convex valuations, we prove that any linearly ordered set can be realized as the difference rank of an ordered difference field.
dc.language.isoen
dc.publisherSpringer International Publishing
dc.source.titleGroups, Modules, and Model Theory - Surveys and Recent Developments.
dc.title.enThe valuation difference rank of an ordered difference field
dc.typeChapitre d'ouvrage
dc.identifier.doi10.1007/978-3-319-51718-6_23
dc.subject.halMathématiques [math]/Logique [math.LO]
dc.identifier.arxiv1301.2611
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.title.proceedingGroups, Modules, and Model Theory - Surveys and Recent Developments.
hal.identifierhal-00947101
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00947101v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.btitle=Groups,%20Modules,%20and%20Model%20Theory%20-%20Surveys%20and%20Recent%20Developments.&rft.date=2017-11-01&rft.au=KUHLMANN,%20Salma&POINT,%20Francoise&MATUSINSKI,%20Mickael&rft.isbn=978-3-319-51717-9&rft.genre=unknown


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