1,720,967 research outputs found
Residually Dominated Groups
No full textWe study the model theory of henselian valued fields of equicharacteristic zero by generalizing results from the complete theory of algebraically closed valued fields (\ACVF) in the literature. Haskell, Hrushovski and Macpherson introduced the notion of \emph{stable domination} which provides a tameness condition to study the model theory of \ACVF.
It was later generalized to \emph{residual domination} in the work by Haskell, Ealy and Simon, and independently by Vicaria for pure henselian valued fields of equicharacteristic zero.
In this thesis, we study residual domination itself, giving characterizations that are similar to those for stably dominated types in \ACVF.
We then introduce \emph{residually dominated groups}, which are the analogue of the \emph{stably dominated groups} introduced and studied extensively by Rideau-Kikuchi and Hrushovski. We show that the connected components of residually dominated groups are subgroups of stably dominated groups that are definable in the algebraic closure of the given henselian valued field. This allows us to extend results from \ACVF to the henselian setting.ThesisCandidate in Philosoph
Definite Forms in Valued Fields
Get PDF Let K = (K, v, ... ) be a model of a model-complete theory, T of valued fields. We
characterise, for certain definable subsets S of K^n, the collections of S-T-integral
definite and S-T-infinitesimal definite rational functions. Specifically, we consider
subsets S defined by both integrality and infinitesimality conditions for the theories of
algebraically closed valued fields, p-adically closed fields, two model-complete theories
of valued D-fields and in two model-complete theories of henselian residually valued
fields.ThesisDoctor of Philosophy (PhD
Types in Algebraically Closed Valued Fields: A Defining Schema for Definable 1-Types
Get PDFIn this thesis we study the types of algebraically closed valued fields (ACVF). We prove the definable types of ACVF are residual and valuational and provide a defining schema for the definable types. We then conclude that all the types are invariant.ThesisMaster of Science (MSc
Explorations in Padic Model Theory
Get PDFThis thesis explores various aspects of the model theory of p-adic fields. It is divided
into two distinct parts. The first part pertains to the theory of P -minimal structures.
The main focus is exploring a class of P -minimal structures which display a certain
tameness property with respect to the approximation of definable functions by their
Taylor polynomials, and builds to a proof of a theorem for passing from local ap-
proximations by Taylor polynomials to global (piecewise-definable) approximations
of functions by their Taylor polynomials in such structures. The final chapter of this
part discusses some aspects of classifying the scope of the class of structures that this
theorem applies to. The second part of the thesis describes a formally verified proof
of Macintyre’s quantifier elimination theorem for p-adic fields in the Isabelle proof
assistant. The algebraic formalisations to required state and prove this theorem are
outlined, including constructions of the p-adic integers and fields, as well as a formally
verified proof of Hensel’s Lemma.DissertationDoctor of Philosophy (PhD)This thesis explores theoretical and computational aspects of the p-adic numbers,
which are fundamental objects of study in number theory. The thesis approaches
these problems using techniques from model theory, which is a branch of mathemat-
ical logic which is particularly effective at analyzing algebraic structures. The thesis
has two parts. The first is purely theoretical and focuses on the proof of a theorem
about p-adic functions which can be defined in certain logical languages. The second
part takes a computational approach and focuses on developing theoretical results
about p-adic numbers using a special software system called a proof assistant (the
particular proof assistant is called Isabelle). By developing theory of p-adics in Is-
abelle, we can use software to automatically verify the correctness of proofs of results
and coherence of definitions. The resulting libraries can then be imported and used
in future developments of machine-verified mathematical theory for more complex
results
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe 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
Model Theory and Valuations
Get PDFThis thesis explores some of the relationships between model theoretic and algebraic properties of fields, focusing on valuations of fields. We first show that the dp-rank of henselian valued fields admitting relative quantifier elimination is equal to the sum of the dp-ranks of the value group and of the residue field. Moreover, we give a characterization of henselianity of valued fields of finite dp-rank in terms of the dp-rank of definable sets. We also obtain partial results generalizing the work of Johnson in classifying fields of finite dp-rank. Finally, we consider fields with the property that the algebraic closure is an immediate extension with respect to every valuation. We show that under certain conditions these fields are dense in their algebraic closure with respect to every valuation and provide an example that demonstrates that this property does not hold in general.ThesisDoctor of Philosophy (PhD
BOUNDING THE DECAY OF P-ADIC OSCILLATORY INTEGRALS WITH A CONSTRUCTIBLE AMPLITUDE FUNCTION AND A SUBANALYTIC PHASE FUNCTION
Get PDFWe obtain an upper bound for decay rate of p-adic oscillatory integrals of with analytic phase function and constructible amplitude map.ThesisDoctor of Philosophy (PhD
Variations on the Author
Get PDF“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
Get PDFWe 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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