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

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:
CreatorsEmailORCID
Sant'Anna, Adonaiadonaisantanna@gmail.com0000-0003-3425-698X
Bueno, Otáviootaviobueno@me.com0000-0002-0251-3032
de França, Márciomarciopalmares@gmail.com0000-0003-1229-6825
Brodzinski, Renatorenatobrodzinski@gmail.com0000-0001-8881-6634
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-dev.library.pitt.edu/id/eprint/18206

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