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## A Dichotomy Principle for Universal Series

### Tom 56 / 2008

Bulletin Polish Acad. Sci. Math. 56 (2008), 93-104 MSC: Primary 05D10, 41A58; Secondary 30B30. DOI: 10.4064/ba56-2-1

#### Streszczenie

Applying results of the infinitary Ramsey theory, namely the dichotomy principle of Galvin–Prikry, we show that for every sequence $(\alpha_{j})_{j=1}^{\infty}$ of scalars, there exists a subsequence $(\alpha_{k_j})_{j=1}^{\infty}$ such that either every subsequence of $(\alpha_{k_j})_{j=1}^{\infty}$ defines a universal series, or no subsequence of $(\alpha_{k_j})_{j=1}^{\infty}$ defines a universal series. In particular examples we decide which of the two cases holds.

#### Autorzy

• V. FarmakiDepartment of Mathematics
Athens University
Panepistemiopolis
15784 Athens, Greece
e-mail
• V. NestoridisDepartment of Mathematics
Athens University
Panepistemiopolis
15784 Athens, Greece
and
Department of Mathematics and Statistics
University of Cyprus
1678 Nicosia, Cyprus
e-mail

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