Flow: the Axiom of Choice is independent from the Partition Principle

Adonai S. Sant'Anna, Otavio Bueno, Marcio P. P. de França, Renato Brodzinski

Published 2020-10-07Version 1

We introduce a general theory of functions called Flow. We prove ZF, non-well founded ZF and ZFC can be immersed within Flow as a natural consequence from our framework. The existence of strongly inaccessible cardinals is entailed from our axioms. And our first important application is the introduction of a model of Zermelo-Fraenkel set theory where the Partition Principle (PP) holds but not the Axiom of Choice (AC). So, Flow allows us to answer to the oldest open problem in set theory: if PP entails AC.