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

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

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arXiv · 2010.03664

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

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

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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.

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Adonai S. Sant'Anna, Otavio Bueno, Marcio P. P. de França, Renato Brodzinski. 2020-10-07. Flow: the Axiom of Choice is independent from the Partition Principle. https://arxiv.org/abs/2010.03664

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