A Dichotomy Principle for Universal Series

V. Farmaki, and V. Nestoridis. "A Dichotomy Principle for Universal Series." Bulletin of the Polish Academy of Sciences. Mathematics 56.2 (2008): 93-104. <http://eudml.org/doc/281182>.

@article{V2008,
abstract = {Applying results of the infinitary Ramsey theory, namely the dichotomy principle of Galvin-Prikry, we show that for every sequence $(α_\{j\})_\{j=1\}^\{∞\}$ of scalars, there exists a subsequence $(α_\{k_j\})_\{j=1\}^\{∞\}$ such that either every subsequence of $(α_\{k_j\})_\{j=1\}^\{∞\}$ defines a universal series, or no subsequence of $(α_\{k_j\})_\{j=1\}^\{∞\}$ defines a universal series. In particular examples we decide which of the two cases holds.},
author = {V. Farmaki, V. Nestoridis},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {universal series; Galvin-Prikry theorem},
language = {eng},
number = {2},
pages = {93-104},
title = {A Dichotomy Principle for Universal Series},
url = {http://eudml.org/doc/281182},
volume = {56},
year = {2008},
}

TY - JOUR
AU - V. Farmaki
AU - V. Nestoridis
TI - A Dichotomy Principle for Universal Series
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2008
VL - 56
IS - 2
SP - 93
EP - 104
AB - Applying results of the infinitary Ramsey theory, namely the dichotomy principle of Galvin-Prikry, we show that for every sequence $(α_{j})_{j=1}^{∞}$ of scalars, there exists a subsequence $(α_{k_j})_{j=1}^{∞}$ such that either every subsequence of $(α_{k_j})_{j=1}^{∞}$ defines a universal series, or no subsequence of $(α_{k_j})_{j=1}^{∞}$ defines a universal series. In particular examples we decide which of the two cases holds.
LA - eng
KW - universal series; Galvin-Prikry theorem
UR - http://eudml.org/doc/281182
ER -