Los axiomas de Zermelo-Fraenkel en la teoría de conjuntos

Abstract

At the Escuela Superior Politécnica de Chimborazo (ESPOCH), in the career of Mathematics there is no complete information, either bibliographic or documentary, that allows a better understanding of the axioms of Zermelo - Fraenkel (ZF) in set theory, they are topics that have not been deepened in the course of this academic career, having deficit in part of their knowledge. The aim is to generate a reference and support document for students through bibliographical reference, in order to make known the study of the axioms of ZF in set theory. This research is based on the qualitative approach, which seeks to understand in a deep and detailed way the subject of study. It is based on evidence collected through the application of specific techniques and methodologies of qualitative research, document analysis and others. The scope of this research is exploratory and descriptive, which means that it seeks to understand and describe the subject without enough information regarding the aforementioned study. In addition, the documentary research design was used as a specific technique to collect data through the review of existing documents. As a result of this analysis we have a reference document entitled “The Zermelo-Fraenkel Axioms in Set Theory” which describes in detail each axiom and its consequences. From the creation of this document two chapters are established: the first one deals with the basic notions of Mathematical Logic, and the second chapter presents the axiomatic ZF in which the ten axioms are exposed with each of their consequences. Since it is a complex subject, there were difficulties and limitations to develop it, in spite of this, a referential document with more important and detailed aspects for its comprehension was made.