Casanovas Ruiz-Fornells, EnriqueMartı́nez Martı́nez, Raúl2021-11-222021-11-222021-01-23https://hdl.handle.net/2445/181380Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2021, Director: Enrique Casanovas Ruiz-Fornells[en] In this work we will prove that the axiom of choice (AC) and the generalized continuum hypothesis (GCH) are consistent with the axioms of Zermelo-Freankel if these are already consistent. For that we will define the concepts of model and relativized formula. With these tools we will be able to give a general proof of relative consistency. Once we have achieved that our purpose will be to find an adequate model so we can apply the general proof and obtain the relative consistency of AC and GCH. The model will be the constructible universe, which is what Gödel originally used to give the consistency proof.55 p.application/pdfspacc-by-nc-nd (c) Raúl Martı́nez Martı́nez, 2021http://creativecommons.org/licenses/by-nc-nd/3.0/es/Teoria de conjuntsTreballs de fi de grauLògica matemàticaAxioma d'eleccióSet theoryBachelor's thesesMathematical logicAxiom of choiceinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess