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Forcing techniques for Cichon’s Maximum: Lecture notes for the mini-course at the University of Vienna
Técnicas de forcing para Cichon Maximal: Notas de un mini-curso en la Universidad de Viena
DOI:
https://doi.org/10.15446/bol.mat.v31n1.121155Palabras clave:
cardinal characteristics of the continuum, Cichon’s diagram, Tukey connections, forcing iteration theory, forcing iterations with ultrafilters and measures, Boolean ultrapowers, forcing intersection with submodels (en)cardinales característicos del continuo, diagrama de Cichon, conexiones de Tukey, teoría de forcing iterado, orcing iterado con ultrafiltros y medidas, ultrapotencias booleanas, intersección de forcing con submodelos (es)
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Cichon’s diagram describes the connections between combinatorial notions related to measure, category, and compactness of sets of irrational numbers. In the second part of the 2010’s, Goldstern, Kellner and Shelah constructed a forcing model of Cichon’s Maximum (meaning that all nondependent cardinal characteristics are pairwise different) by using large cardinals. Some years later, we eliminated this large cardinal assumption. In this mini-course, we explore the forcing techniques to construct the Cichon’s Maximum model and much more.
El diagrama de Cichon describe las conexiones entre nociones combinatorias relacionadas con medida, categoría y compacidad de conjuntos de irracionales. En la segunda mitad de la década del 2010, Goldstern, Kellner y Shelah construyeron un modelo de forcing de Cichon Maximal (i.e. los valores no dependientes de los cardinales característicos del diagrama de Cichon son diferentes dos a dos) usando grandes cardinales. Algunos años más tarde, eliminamos la hipótesis de grandes cardinales. En este mini-curso, exploramos las técnicas de forcing para construir el modelo de Cichon Maximal y mucho más.
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