Ideal independence, free sequences, and the ultrafilter number

Selker, Kevin. "Ideal independence, free sequences, and the ultrafilter number." Commentationes Mathematicae Universitatis Carolinae 56.1 (2015): 117-124. <http://eudml.org/doc/269883>.

@article{Selker2015,
abstract = {We make use of a forcing technique for extending Boolean algebras. The same type of forcing was employed in Baumgartner J.E., Komjáth P., Boolean algebras in which every chain and antichain is countable, Fund. Math. 111 (1981), 125–133, Koszmider P., Forcing minimal extensions of Boolean algebras, Trans. Amer. Math. Soc. 351 (1999), no. 8, 3073–3117, and elsewhere. Using and modifying a lemma of Koszmider, and using CH, we obtain an atomless BA, $A$ such that $\mathfrak \{f\}(A) = \text\{s\}_\{\text\{mm\}\}(A) <\mathfrak \{u\}(A)$, answering questions raised by Monk J.D., Maximal irredundance and maximal ideal independence in Boolean algebras, J. Symbolic Logic 73 (2008), no. 1, 261–275, and Monk J.D., Maximal free sequences in a Boolean algebra, Comment. Math. Univ. Carolin. 52 (2011), no. 4, 593–610.},
author = {Selker, Kevin},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {free sequences; Boolean algebras; cardinal functions; ultrafilter number; free sequences; Boolean algebras; cardinal functions; ultrafilter number},
language = {eng},
number = {1},
pages = {117-124},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Ideal independence, free sequences, and the ultrafilter number},
url = {http://eudml.org/doc/269883},
volume = {56},
year = {2015},
}

TY - JOUR
AU - Selker, Kevin
TI - Ideal independence, free sequences, and the ultrafilter number
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2015
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 56
IS - 1
SP - 117
EP - 124
AB - We make use of a forcing technique for extending Boolean algebras. The same type of forcing was employed in Baumgartner J.E., Komjáth P., Boolean algebras in which every chain and antichain is countable, Fund. Math. 111 (1981), 125–133, Koszmider P., Forcing minimal extensions of Boolean algebras, Trans. Amer. Math. Soc. 351 (1999), no. 8, 3073–3117, and elsewhere. Using and modifying a lemma of Koszmider, and using CH, we obtain an atomless BA, $A$ such that $\mathfrak {f}(A) = \text{s}_{\text{mm}}(A) <\mathfrak {u}(A)$, answering questions raised by Monk J.D., Maximal irredundance and maximal ideal independence in Boolean algebras, J. Symbolic Logic 73 (2008), no. 1, 261–275, and Monk J.D., Maximal free sequences in a Boolean algebra, Comment. Math. Univ. Carolin. 52 (2011), no. 4, 593–610.
LA - eng
KW - free sequences; Boolean algebras; cardinal functions; ultrafilter number; free sequences; Boolean algebras; cardinal functions; ultrafilter number
UR - http://eudml.org/doc/269883
ER -