Geodesic
A Dichotomy Principle for Universal Series
V. Farmaki 1   ; V. Nestoridis 2
1 Department of Mathematics Athens University Panepistemiopolis 15784 Athens, Greece
2 Department of Mathematics Athens University Panepistemiopolis 15784 Athens, Greece and Department of Mathematics and Statistics University of Cyprus 1678 Nicosia, Cyprus
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 56 (2008) no. 2, pp. 93-104 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/ba56-2-1
Keywords: applying results infinitary ramsey theory namely dichotomy principle galvin prikry every sequence alpha infty scalars there exists subsequence alpha infty either every subsequence alpha infty defines universal series subsequence alpha infty defines universal series particular examples decide which cases holds

V. Farmaki  1   ; V. Nestoridis  2

1 Department of Mathematics Athens University Panepistemiopolis 15784 Athens, Greece
2 Department of Mathematics Athens University Panepistemiopolis 15784 Athens, Greece and Department of Mathematics and Statistics University of Cyprus 1678 Nicosia, Cyprus 
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V. Farmaki; V. Nestoridis. A Dichotomy Principle for Universal Series. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 56 (2008) no. 2, pp. 93-104. doi: 10.4064/ba56-2-1

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