ABSTRACT
As the last chapter in this book, in the following we will see how we can rebuild the system of mathematics where only potential infinities are allowed.
This chapter is organized as follows. Section 12.1 lays out a detailed plan for such a desired system by formulating the formal basis of the necessary philosophical, logical, and set theoretic foundations. Section 12.2 addresses several open problems about the infinity between predicates and infinite sets. In the final section, 12.3, we consider the intension and structure of actually infinite, rigid sets.
