1,720,966 research outputs found
Ordered Algebraic Structures : Hahn Fields, Convex Valuations, and Exponentials
No full textThis habilitation thesis contains seven articles dedicated to the valuation and model theoretic study of ordered algebraic structures. It is divided into three parts, each consisting of those articles focussing on a particular class of structures: Hahn fields, definable convex valuations in ordered fields, and ordered exponential fields.
In the first part, substructures of fields of generalised power series are investigated. These substructures, mostly subfields, are either induced by families of prescribed supports or solution sets of generalised linear recurrence equations.
The second part undertakes a systematic study of first-order definable convex valuation rings in ordered fields, mostly dealing with the henselian case. Several definability results are established that rely on (topological) conditions on the residue field and on the value group of the valuations.
The third part is concerned with models of real exponentiation, that is, ordered exponential fields that are elementarily equivalent to the real exponential field. The two main threads in this part are integer parts of such models as well as prime models of real exponentiation.publishe
Value Groups and Residue Fields of Models of Real Exponentiation
No full textLet F be an archimedean field, G a divisible ordered abelian group and h a group exponential on G. A triple (F,G,h) is realised in a non-archimedean exponential field (K,exp) if the residue field of K under the natural valuation is F and the induced exponential group of (K,exp) is (G,h). We give a full characterisation of all triples (F,G,h) which can be realised in a model of real exponentiation in the following two cases: i) G is countable. ii) G is of cardinality kappa and kappa-saturated for an uncountable regular cardinal kappa with kappa^(<kappa) = kappa.publishe
Embedding the prime model of real exponentiation into o-minimal exponential fields
No full textMotivated by the decidability question for the theory of real exponentiation
and by the Transfer Conjecture for o-minimal exponential fields, we show that,
under the assumption of Schanuel's Conjecture, the prime model of real
exponentiation is embeddable into any o-minimal exponential field, where the
embedding is not necessarily elementary. This is a consequence of an
unconditional model theoretic embeddability result that we obtain by applying
K\H{o}nig's Lemma.Comment: 7 page
Ordered transexponential fields
No full textWe develop a first-order theory of ordered transexponential fields in the
language , where and stand for unary function
symbols. While the archimedean models of this theory are readily described, the
study of the non-archimedean models leads to a systematic examination of the
induced structure on the residue field and the value group under the natural
valuation. We establish necessary and sufficient conditions on the value group
of an ordered exponential field to admit a transexponential function
compatible with . Moreover, we give a full characterisation of all
countable ordered transexponential fields in terms of their valuation theoretic
invariants.Comment: 26 pages, including 2 figure
Models of true arithmetic are integer parts of models of real exponentation
No full textExploring further the connection between exponentiation on real closed fields and the existence of an integer part modelling strong fragments of arithmetic, we demonstrate that each model of true arithmetic is an integer part of an exponential real closed field that is elementarily equivalent to the real numbers with exponentiation and that each model of Peano arithmetic is an integer part of a real closed field that admits an isomorphism between its ordered additive and its ordered multiplicative group of positive elements. Under the assumption of Schanuel’s Conjecture, we obtain further strengthenings for the last statement.publishe
Going Beyond Counting First Authors in Author Co-citation Analysis
No full textThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
No full text“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
No full textWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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