Cardinal invariants associated with ideals between measure zero and strong measure zero

In 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.

• Autores: Cardona Montoya, Miguel Antonio
• Fecha de publicación: 2016
• Institución: Universidad Nacional de Colombia
• Repositorio: Universidad Nacional de Colombia
• Idioma: spa
• OAI Identifier: oai:repositorio.unal.edu.co:unal/58776
• Acceso en línea: https://repositorio.unal.edu.co/handle/unal/58776; http://bdigital.unal.edu.co/55706/
• Palabra clave: 51 Matemáticas / Mathematics; Itearations with finite support; Model of ZFC; Yorioka ideal; Preservation theory; Matrix iterations; Cardinal invariants
• Rights: openAccess
• License: Atribución-NoComercial 4.0 Internacional