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tfg_fernandez_dejean_anton.pdf (538.48 KB)

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Bachelor thesis

Publication date

2022-06-13

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cc-by-nc-nd (c) Anton Fernàndez Dejean, 2022
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/189975

The consistency of the negation of the Continuum Hypothesis

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Abstract

[en] The purpose of this work is to prove the consistency of the negation of the Continuum Hypothesis $(\mathrm{CH})$ with the Zermelo - Fraenkel axiomatic system, including the Axiom of Choice (ZFC). The Continuum Hypothesis states that there is no set whose cardinality is strictly between the cardinality of the set of integers and the cardinality of the set of real numbers. It is well-known that $C H$ is independent of ZFC: neither $C H$ nor its negation can be proved from ZFC. In order to show the consistency of $\neg C H$, we will use the method of forcing that permits us to construct a model that satisfies all the axioms of $Z F C$ and where $C H$ fails.

Description

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2022, Director: Juan Carlos Martínez Alonso

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Teoria de conjunts, Treballs de fi de grau, Lògica matemàtica, Forcing (Teoria de models)

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Set theory, Bachelor's theses, Mathematical logic, Forcing (Model theory)

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Treballs Finals de Grau (TFG) - Matemàtiques

Citation

FERNÀNDEZ DEJEAN, Anton. The consistency of the negation of the Continuum Hypothesis. [consulted: 11 of June of 2026]. Available at: https://hdl.handle.net/2445/189975

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