A Dichotomy Principle for Universal Series
Volume 56 / 2008
Bulletin Polish Acad. Sci. Math. 56 (2008), 93-104
MSC: Primary 05D10, 41A58; Secondary 30B30.
DOI: 10.4064/ba56-2-1
Abstract
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.
