Strong sequences and partition relations

Joanna Jureczko

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica (2017)

  • Volume: 16, Issue: 1, page 51-59
  • ISSN: 2300-133X

Abstract

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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.

How to cite

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Joanna Jureczko. "Strong sequences and partition relations." Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica 16.1 (2017): 51-59. <http://eudml.org/doc/288453>.

@article{JoannaJureczko2017,
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.},
author = {Joanna Jureczko},
journal = {Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica},
keywords = {Strong sequences; Erdös-Rado theorem; partition relations; inaccessible cardinals; singular cardinals},
language = {eng},
number = {1},
pages = {51-59},
title = {Strong sequences and partition relations},
url = {http://eudml.org/doc/288453},
volume = {16},
year = {2017},
}

TY - JOUR
AU - Joanna Jureczko
TI - Strong sequences and partition relations
JO - Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
PY - 2017
VL - 16
IS - 1
SP - 51
EP - 59
AB - 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.
LA - eng
KW - Strong sequences; Erdös-Rado theorem; partition relations; inaccessible cardinals; singular cardinals
UR - http://eudml.org/doc/288453
ER -

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