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Origen y desarrollo de la teoría de modelos núcleo II
Origin and development of the theory of core models II
DOI:
https://doi.org/10.15446/bol.mat.v31n1.121298Palabras clave:
Teoría de conjuntos, Modelos internos, Teoría de modelos núcleo, Grandes cardinales, Sucesiones de medidas, Teoremas de cubierta, Extensores, Sostenidos (es)Set theory, Inner Models, Core model theory, Large Cardinals, Sequences of measures, Covering Theorem, Extenders, Sharps (en)
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En esta segunda parte continuamos con los objetivos propuestos en la primera, pero esta vez nos encargamos de modelos núcleo superiores a KDJ, es decir, aquellos que pueden contener cardinales medibles o mayores. Se inicia con un examen de la construcción de ultrapotencias del universo mediante un extensor visto como un límite directo. Parte importante de esta descripción es ilustrar mediante cardinales fuertes los requerimientos para lograr un modelo interno con un cardinal de este tipo. Se discute la propiedad de cubierta para modelos núcleo de orden superior. A continuación se examinan las dificultades para construir modelos núcleo debajo de un cardinal Woodin, la noción de árbol de iteración, y la influencia de los cardinales Woodin en este concepto. Finalmente se examina el estado actual de la teoría y se resume la noción de modelo núcleo.
For this second part, we continue with the proposed goals in the first part. Now we deal with higher than KDJ core models. That is, core models that allow large cardinals like measurables or higher. We begin by studying extender ultrapowers of the universe as a direct limit. The importance of this study is to illustrate, with strong cardinals, the requirements to construct an inner model with these cardinals. We discuss the covering property for higherorder core models. Next, we assess the hardships of constructing core models below a Woodin cardinal. We discuss the concept of iteration trees and the Woodin cardinal influence for iteration trees. Finally, we examine the current status of the subject and gather the core model notion.
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