Author:
CANCINO JONATHAN,GUZMÁN OSVALDO,MILLER ARNOLD W.
Abstract
AbstractWe say that
$\mathcal {I}$
is an ideal independent family if no element of
${\mathcal {I}}$
is a subset mod finite of a union of finitely many other elements of
${\mathcal {I}}.$
We will show that the minimum size of a maximal ideal independent family is consistently bigger than both
$\mathfrak {d}$
and
$\mathfrak {u},$
this answers a question of Donald Monk.
Publisher
Cambridge University Press (CUP)
Reference16 articles.
1. Mad families and ultrafilters;Brendle;Acta Universitatis Carolinae, Mathematica et Physica,2007
2. [8] Guzmán, O. and Hrušák, M. , Parametrized $\diamondsuit$ -principles and canonical models. Slides from Retrospective Workshop on Forcing and its Applications, Fields Institute, 2015.
3. Diamond principles in Cichoń’s diagram
4. Zapping small filters
5. Free sequences in $${\mathscr {P}}\left( \omega \right) /\text {fin}$$