Flow: the Axiom of Choice is independent from the Partition Principle
Logic
2020-10-09 v1
Abstract
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.
Keywords
Cite
@article{arxiv.2010.03664,
title = {Flow: the Axiom of Choice is independent from the Partition Principle},
author = {Adonai S. Sant'Anna and Otavio Bueno and Marcio P. P. de França and Renato Brodzinski},
journal= {arXiv preprint arXiv:2010.03664},
year = {2020}
}
Comments
37 pages, 4 Figures