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memoria.pdf (455.97 KB)

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Bachelor thesis

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2017-06-29

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cc-by-nc-nd (c) Gina Garcia Tarrach, 2017
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/121981

The axiom of choice and its implications in mathematics

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[en] The Axiom of Choice is an axiom of set theory which states that, given a collection of non-empty sets, it is possible to choose an element out of each set of the collection. The implications of the acceptance of the Axiom are many, some of them essential to the development of contemporary mathematics. In this work, we give a basic presentation of the Axiom and its consequences: we study the Axiom of Choice as well as some of its equivalent forms such as the Well Ordering Theorem and Zorn’s Lemma, some weaker choice principles, the implications of the Axiom in different fields of mathematics, some paradoxical results implied by it, and its role within the Zermelo-Fraenkel axiomatic theory.

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Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2017, Director: Joan Bagaria

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Axioma d'elecció, Treballs de fi de grau, Teoria de conjunts, Anàlisi matemàtica, Lògica matemàtica, Topologia, Teoria de grafs

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Axiom of choice, Bachelor's theses, Set theory, Mathematical analysis, Mathematical logic, Topology, Graph theory

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Treballs Finals de Grau (TFG) - Matemàtiques

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GARCIA TARRACH, Gina. The axiom of choice and its implications in mathematics. [consulted: 9 of October of 2026]. Available at: https://hdl.handle.net/2445/121981

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