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Valued fields

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This book addresses a gap in the model-theoretic understanding of valued fields that had limited the interactions of model theory with geometry. It contains significant developments in both pure and applied model theory. Part I of the book is a study of stably dominated types. These form a subset of the type space of a theory that behaves in many ways like the space of types in a stable theory. This part begins with an introduction to the key ideas of stability theory for stably dominated types. Part II continues with an outline of some classical results in the model theory of valued fields and explores the application of stable domination to algebraically closed valued fields. The research presented here is made accessible to the general model theorist by the inclusion of the introductory sections of each part.

Model theory --- Valued fields --- Domination (Graph theory) --- Model theory. --- Valued fields. --- Graph theory --- Fields, Valued --- Topological fields --- Logic, Symbolic and mathematical

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Mathematical logic --- p-adic numbers --- Algebraic fields --- Transfer functions --- Valued fields --- Fields, Valued --- Topological fields --- Functions, Transfer --- Automatic control --- Control theory --- Algebraic number fields --- Algebraic numbers --- Fields, Algebraic --- Algebra, Abstract --- Algebraic number theory --- Rings (Algebra) --- Numbers, p-adic --- Number theory --- p-adic analysis --- Algebraic fields. --- Transfer functions. --- Fonctions de transfert. --- p-adic numbers. --- Nombres p-adiques. --- Valued fields. --- Corps valués.

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Teleparallel Gravity (TG) is an alternative theory for gravitation, which is equivalent to General Relativity (GR). However, it is conceptually different. For example in GR geometry replaces the concept of force, and the trajectories are determined by geodesics. TG attributes gravitation to torsion, which accounts for gravitation by acting as a force. TG has already solved some old problems of gravitation (like the energy-momentum density of the gravitational field). The interest in TG has grown in the last few years. The book here proposed will be the first one dedicated exclusively to TG, and will include the foundations of the theory, as well as applications to specific problems to illustrate how the theory works.

Field theory (Physics). --- Valued fields. --- Gravitation --- Gauge fields (Physics) --- Physics --- Physical Sciences & Mathematics --- Atomic Physics --- Gravitation. --- Fields, Gauge (Physics) --- Gage fields (Physics) --- Gauge theories (Physics) --- Physics. --- Differential geometry. --- Mathematical physics. --- Classical and Quantum Gravitation, Relativity Theory. --- Differential Geometry. --- Mathematical Methods in Physics. --- Mathematical Physics. --- Field theory (Physics) --- Matter --- Antigravity --- Centrifugal force --- Relativity (Physics) --- Properties --- Group theory --- Symmetry (Physics) --- Global differential geometry. --- Physical mathematics --- Geometry, Differential --- Mathematics --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Differential geometry