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(...
- Autores:
-
Cardona Montoya, Miguel Antonio
- Tipo de recurso:
- 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
| Summary: | 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. |
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