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.Comment: 37 pages, 4 Figure
