Sant'Anna, Adonai and Bueno, Otávio and de França, Márcio and Brodzinski, Renato (2020) Flow: the Axiom of Choice is independent from the Partition Principle. [Preprint]

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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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Item Type:	Preprint
Creators:	Creators Email ORCID Sant'Anna, Adonai adonaisantanna@gmail.com 0000-0003-3425-698X Bueno, Otávio otaviobueno@me.com 0000-0002-0251-3032 de França, Márcio marciopalmares@gmail.com 0000-0003-1229-6825 Brodzinski, Renato renatobrodzinski@gmail.com 0000-0001-8881-6634
Keywords:	Sets, functions, axiom of choice, partition principle
Subjects:	Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic
Depositing User:	Adonai Sant'Anna
Date Deposited:	09 Oct 2020 17:41
Last Modified:	09 Oct 2020 17:41
Item ID:	18206
Subjects:	Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic
Date:	10 October 2020
URI:	https://philsci-archive.pitt.edu/id/eprint/18206

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