Hrušák, Michael, and Meza-Alcántara, David. "Comparison game on Borel ideals." Commentationes Mathematicae Universitatis Carolinae 52.2 (2011): 191-204. <http://eudml.org/doc/246623>.
@article{Hrušák2011,
abstract = {We propose and study a “classification” of Borel ideals based on a natural infinite game involving a pair of ideals. The game induces a pre-order $\sqsubseteq $ and the corresponding equivalence relation. The pre-order is well founded and “almost linear”. We concentrate on $F_\{\sigma \}$ and $F_\{\sigma \delta \}$ ideals. In particular, we show that all $F_\{\sigma \}$-ideals are $\sqsubseteq $-equivalent and form the least equivalence class. There is also a least class of non-$F_\{\sigma \}$ Borel ideals, and there are at least two distinct classes of $F_\{\sigma \delta \}$ non-$F_\{\sigma \}$ ideals.},
author = {Hrušák, Michael, Meza-Alcántara, David},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {ideals on countable sets; comparison game; Tukey order; games on integers; ideals on countable sets; comparison game; Tukey order; games on integers},
language = {eng},
number = {2},
pages = {191-204},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Comparison game on Borel ideals},
url = {http://eudml.org/doc/246623},
volume = {52},
year = {2011},
}
TY - JOUR
AU - Hrušák, Michael
AU - Meza-Alcántara, David
TI - Comparison game on Borel ideals
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2011
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 52
IS - 2
SP - 191
EP - 204
AB - We propose and study a “classification” of Borel ideals based on a natural infinite game involving a pair of ideals. The game induces a pre-order $\sqsubseteq $ and the corresponding equivalence relation. The pre-order is well founded and “almost linear”. We concentrate on $F_{\sigma }$ and $F_{\sigma \delta }$ ideals. In particular, we show that all $F_{\sigma }$-ideals are $\sqsubseteq $-equivalent and form the least equivalence class. There is also a least class of non-$F_{\sigma }$ Borel ideals, and there are at least two distinct classes of $F_{\sigma \delta }$ non-$F_{\sigma }$ ideals.
LA - eng
KW - ideals on countable sets; comparison game; Tukey order; games on integers; ideals on countable sets; comparison game; Tukey order; games on integers
UR - http://eudml.org/doc/246623
ER -
