Abstract

The objective of this document is to present three introductory notes on set theory: The first note presents an overview of this discipline from its origins to the present, in the second note some considerations are made about the evaluation of reasoning applying the first-order Logic and Löwenheim's theorems, Church Indecidibility, Completeness and Incompleteness of Gödel, it is known that the axiomatic theories of most commonly used sets are written in a specific first-order language, that is, they are developed within the framework of first-order logic, so this note is relevant; and the third note refers to the presence of mathematical platonism in the axioms of ZFC and in the axioms of "complete ordered field", it is known that the last axioms mentioned characterize (except isomorphism) the real number system and are currently used to develop the real Analysis in the context of set theory. It is hoped that this article will be of pedagogical utility for students interested in set theory and in the philosophy of mathematics (that are beginning in the subject).