Atribución-NoComercial 4.0 InternacionalMejía Guzman, Diego AlejandroBlázquez Sanz, DavidCardona Montoya, Miguel Antonio2019-07-022019-07-022016https://repositorio.unal.edu.co/handle/unal/58776In 2002, Yorioka [Y02] introduced the sigma-ideal I_f for increasing functions f from omega to omega to analyze the cofinality of the strong measure zero ideal. We use and generalize some techiques of itearations with finite support to construct a model of ZFC, by a matrix iteration, satisfying add(I_f ) cov(I_f ) non(I_f ) cof(I_f ) for every fast increasing f. One technical tool we use is the preservation theory of Judah-Shelah [JS90] and Brendle [Br91]. We generalize this theory so that we can cover the example of preservation presented in [KO14] which is fundamental in this thesis. We also provide original proofs of two Claims from [O08], about the additivity and cofinality of Yorioka ideals, whose proofs have not been published anywhere.application/pdfspaDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/51 Matemáticas / MathematicsTrabajo de grado - Maestríahttp://bdigital.unal.edu.co/55706/info:eu-repo/semantics/openAccessItearations with finite supportModel of ZFCYorioka idealPreservation theoryMatrix iterationsCardinal invariants