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κ-strong sequences and the existence of generalized independent families

100%

Jureczko J.

Open Mathematics

2017

tom 15

nr 1

1277-1282

In this paper we will show some relations between generalized versions of strong sequences introduced by Efimov in 1965 and independent families. We also show some inequalities between cardinal invariants associated with these both notions.

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Strong sequences and partition relations

88%

Jureczko J.

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

2017

tom 16

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.

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1 Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

1 Open Mathematics

2 Jureczko J.

2 2017

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κ-strong sequences and the existence of generalized independent families

Strong sequences and partition relations