Geodesic
Ideal independence, free sequences, and the ultrafilter number
Commentationes Mathematicae Universitatis Carolinae, Tome 56 (2015) no. 1, pp. 117-124.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 $\mathfrak{f}(A) = \text{s}_{\text{mm}}(A) \frak{u}(A)$, 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.
DOI : 10.14712/1213-7243.015.110
Classification : 06E05, 54A25
Keywords: free sequences; Boolean algebras; cardinal functions; ultrafilter number 
@article{10_14712_1213_7243_015_110,
     author = {Selker, Kevin},
     title = {Ideal independence, free sequences, and the ultrafilter number},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {117--124},
     publisher = {mathdoc},
     volume = {56},
     number = {1},
     year = {2015},
     doi = {10.14712/1213-7243.015.110},
     mrnumber = {3311582},
     zbl = {06433810},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.015.110/}
}
TY  - JOUR
AU  - Selker, Kevin
TI  - Ideal independence, free sequences, and the ultrafilter number
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2015
SP  - 117
EP  - 124
VL  - 56
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.015.110/
DO  - 10.14712/1213-7243.015.110
LA  - en
ID  - 10_14712_1213_7243_015_110
ER  - 
%0 Journal Article
%A Selker, Kevin
%T Ideal independence, free sequences, and the ultrafilter number
%J Commentationes Mathematicae Universitatis Carolinae
%D 2015
%P 117-124
%V 56
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.015.110/
%R 10.14712/1213-7243.015.110
%G en
%F 10_14712_1213_7243_015_110
Selker, Kevin. Ideal independence, free sequences, and the ultrafilter number. Commentationes Mathematicae Universitatis Carolinae, Tome 56 (2015) no. 1, pp. 117-124. doi : 10.14712/1213-7243.015.110. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.015.110/

Cité par Sources :