Rothberger gaps in fragmented ideals

Jörg Brendle, and Diego Alejandro Mejía. "Rothberger gaps in fragmented ideals." Fundamenta Mathematicae 227.1 (2014): 35-68. <http://eudml.org/doc/283367>.

@article{JörgBrendle2014,
abstract = {The Rothberger number (ℐ) of a definable ideal ℐ on ω is the least cardinal κ such that there exists a Rothberger gap of type (ω,κ) in the quotient algebra (ω)/ℐ. We investigate (ℐ) for a class of $F_\{σ\}$ ideals, the fragmented ideals, and prove that for some of these ideals, like the linear growth ideal, the Rothberger number is ℵ₁, while for others, like the polynomial growth ideal, it is above the additivity of measure. We also show that it is consistent that there are infinitely many (even continuum many) different Rothberger numbers associated with fragmented ideals.},
author = {Jörg Brendle, Diego Alejandro Mejía},
journal = {Fundamenta Mathematicae},
keywords = {quotients of ideals on $\omega $; Rothberger gaps; fragmented ideals; (un)bounding number; additivity of the null ideal},
language = {eng},
number = {1},
pages = {35-68},
title = {Rothberger gaps in fragmented ideals},
url = {http://eudml.org/doc/283367},
volume = {227},
year = {2014},
}

TY - JOUR
AU - Jörg Brendle
AU - Diego Alejandro Mejía
TI - Rothberger gaps in fragmented ideals
JO - Fundamenta Mathematicae
PY - 2014
VL - 227
IS - 1
SP - 35
EP - 68
AB - The Rothberger number (ℐ) of a definable ideal ℐ on ω is the least cardinal κ such that there exists a Rothberger gap of type (ω,κ) in the quotient algebra (ω)/ℐ. We investigate (ℐ) for a class of $F_{σ}$ ideals, the fragmented ideals, and prove that for some of these ideals, like the linear growth ideal, the Rothberger number is ℵ₁, while for others, like the polynomial growth ideal, it is above the additivity of measure. We also show that it is consistent that there are infinitely many (even continuum many) different Rothberger numbers associated with fragmented ideals.
LA - eng
KW - quotients of ideals on $\omega $; Rothberger gaps; fragmented ideals; (un)bounding number; additivity of the null ideal
UR - http://eudml.org/doc/283367
ER -