Elaboración de una monografía sobre la eliminación de cuantificadores, dirigida a estudiantes de la carrera de Matemática de la ESPOCH

Abstract

ESPOCH does not have any evidence on the existence of information regarding quantifier elimination, which impedes students interested in classifying and building mathematical structures to initiate their research. Therefore, the aim of this research was to perform an analysis on the theory of quantifier elimination by presenting definitions, examples and proof of theorems, in order to develop a monograph to be used as bibliographic material for students of Mathematics at ESPOCH, and all those students interested in understanding this topic. The methodology implemented had a qualitative approach and used a descriptive study to analyze and describe the most relevant topics on quantifier elimination. In addition, a documentary type design was applied, since it implied a process based on the search, recovery and critical analysis of relevant contents. By means of this methodology it was possible to determine that the quantifier elimination technique helpsin the simplification process mathematical logic, model theory and theory of computation. It was possible to evidence that certain theories admit quantifier elimination, making it easier to demonstrate that such theories are decidable, definable and complete. In this context it is concluded that the quantifier elimination technique greatly synthesizes the study of theories that have properties such as decidability, definability and completeness.