Strong sequences and partition relations

• Main Author: Joanna Jureczko
• Format: Article
• Language: deu
• Published: Wydawnictwo Naukowe Uniwersytetu Pedagogicznego 2017-12-01
• Series: Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica
• Subjects: Strong sequences; Erdős-Rado theorem; partition relations; inaccessible cardinals; singular cardinals
• Online Access: http://studmath.up.krakow.pl/index.php/studmath/article/view/217

The first result in partition relations topic belongs to Ramsey (1930). Since that this topic has been still explored. Probably the most famous partition theorem is Erdős-Rado theorem (1956). On the other hand in 60's of the last century Efimov introduced strong sequences method, which was used for proving some famous theorems in dyadic spaces. The aim of this paper is to generalize theorem on strong sequences and to show that it is equivalent to generalized version of well-known Erdős-Rado theorem. It will be also shown that this equivalence holds for singulars. Some applications and conclusions will be presented too.