<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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 Erdös-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 Erdös-Rado theorem. It will be also shown that this equivalence holds for singulars. Some applications and conclusions will be presented too.</p></abstract>

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 Erdös-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 Erdös-Rado theorem. It will be also shown that this equivalence holds for singulars. Some applications and conclusions will be presented too.

Strong sequences and partition relations

Wrocław University of Science and Technology

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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{"article-title":"Strong sequences and partition relations"}

The first result in partition relations topic belongs to Ramsey (1930). Since that this topic has been still explored. Probably the most famous partition...

Strong sequences and partition relations

Published Online: Jan 27, 2018

Page range: 51 - 59

Received: Feb 28, 2016

Accepted: Aug 26, 2017

DOI: https://doi.org/10.1515/aupcsm-2017-0004

Keywords
Strong sequences, Erdös-Rado theorem, partition relations, inaccessible cardinals, singular cardinals

© 2017 Joanna Jureczko, published by De Gruyter Open

This work is licensed under a Creative Commons Attribution Share-Alike 4.0 License.

Strong sequences and partition relations

Published Online: Jan 27, 2018

Page range: 51 - 59

Received: Feb 28, 2016

Accepted: Aug 26, 2017

DOI: https://doi.org/10.1515/aupcsm-2017-0004

KeywordsStrong sequences, Erdös-Rado theorem, partition relations, inaccessible cardinals, singular cardinals

© 2017 Joanna Jureczko, published by De Gruyter Open

This work is licensed under a Creative Commons Attribution Share-Alike 4.0 License.

Keywords
Strong sequences, Erdös-Rado theorem, partition relations, inaccessible cardinals, singular cardinals