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| Main Authors: | , |
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| Format: | Recurso digital |
| Language: | |
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Zenodo
2025
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| Online Access: | https://doi.org/10.5281/zenodo.17845724 |
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Table of Contents:
- <p>This paper presents a comparative theoretical analysis of several weak forms of the Axiom of Choice (AC) and<br>their logical consequences within the framework of Zermelo–Fraenkel Set Theory (ZF). While the full Axiom of<br>Choice ensures the existence of a global choice function for all families of nonempty sets, weaker variants such<br>as the Axiom of Countable Choice, the Axiom of Dependent Choice, and the Boolean Prime Ideal Theorem<br>capture limited but significant forms of selection. Through model-theoretic and proof-theoretic examinations,<br>this study highlights the relative strength, independence, and interrelations among these axioms. The findings<br>affirm that while these principles are equivalent in ZFC, their logical independence in ZF reveals an order of<br>choice principles. This comparative analysis deepens understanding of how restricted forms of choice operate<br>and clarifies the structural role of AC in modern set-theoretic foundations.</p>