Martínez Alonso, Juan CarlosFernàndez Dejean, Anton2022-10-192022-10-192022-06-13https://hdl.handle.net/2445/189975Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2022, Director: Juan Carlos Martínez Alonso[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.55 p.application/pdfengcc-by-nc-nd (c) Anton Fernàndez Dejean, 2022http://creativecommons.org/licenses/by-nc-nd/3.0/es/Teoria de conjuntsTreballs de fi de grauLògica matemàticaForcing (Teoria de models)Set theoryBachelor's thesesMathematical logicForcing (Model theory)info:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess