On the theory of the logarithmic transseries field as an ordered valued logarithmic field

"In this work we focus on the study of the first order theory of the logarithmic transseries field T_log as an ordered valued logarithmic field, which is conjectured to have a good model theory. As a first step in such direction, we study the theory of T_log as an ordered valued field with restricted analytic functions and a partial exponential function defined in the valuation ring. Among other things, we show that this theory is model complete and complete. In the same spirit, we also consider a class of Hahn fields equipped with a convex valuation ring and a partial exponential function defined in the valuation ring, and we show an Ax-Kochen-Ershov type equivalence theorem for this class of structures. As a second step, we study the theory of the structure induced by the logarithm of T_log in its value group and we prove the model completeness and completeness of this theory. Finally, we use the previous work to propose a theory of ordered valued logarithmic fields, we show that T_log can be expanded to a model of this theory and state some conjectures that would prove the model completeness."--Tomado del Formato de Documento de Grado.

• Autores: Angel Bautista, José Leonardo
• Tipo de recurso: Doctoral thesis
• Fecha de publicación: 2019
• Institución: Universidad de los Andes
• Repositorio: Séneca: repositorio Uniandes
• Idioma: eng
• OAI Identifier: oai:repositorio.uniandes.edu.co:1992/41292
• Acceso en línea: http://hdl.handle.net/1992/41292
• Palabra clave: Logaritmos - Investigaciones; Teoría de modelos - Investigaciones; Funciones exponenciales - Investigaciones; Matemáticas
• Rights: openAccess
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/