Geodesic
Splitting Families and Complete Separability
Canadian mathematical bulletin, Tome 57 (2014) no. 1, pp. 119-124

Voir la notice de l'article provenant de la source Cambridge University Press

We answer a question from Raghavan and Steprāns by showing that $\mathfrak{s}\,\text{=}\,{{\mathfrak{s}}_{\omega ,\omega }}.$ Then we use this to construct a completely separable maximal almost disjoint family under $\mathfrak{s}\,\le \,\mathfrak{a}$ , partially answering a question of Shelah.
DOI : 10.4153/CMB-2013-027-2
Mots-clés : 03E05, 03E17, 03E65, maximal almost disjoint family, cardinal invariants 
Mildenberger, Heike; Raghavan, Dilip; Steprans, Juris. Splitting Families and Complete Separability. Canadian mathematical bulletin, Tome 57 (2014) no. 1, pp. 119-124. doi: 10.4153/CMB-2013-027-2
@article{10_4153_CMB_2013_027_2,
     author = {Mildenberger, Heike and Raghavan, Dilip and Steprans, Juris},
     title = {Splitting {Families} and {Complete} {Separability}},
     journal = {Canadian mathematical bulletin},
     pages = {119--124},
     year = {2014},
     volume = {57},
     number = {1},
     doi = {10.4153/CMB-2013-027-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2013-027-2/}
}
TY  - JOUR
AU  - Mildenberger, Heike
AU  - Raghavan, Dilip
AU  - Steprans, Juris
TI  - Splitting Families and Complete Separability
JO  - Canadian mathematical bulletin
PY  - 2014
SP  - 119
EP  - 124
VL  - 57
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2013-027-2/
DO  - 10.4153/CMB-2013-027-2
ID  - 10_4153_CMB_2013_027_2
ER  - 
%0 Journal Article
%A Mildenberger, Heike
%A Raghavan, Dilip
%A Steprans, Juris
%T Splitting Families and Complete Separability
%J Canadian mathematical bulletin
%D 2014
%P 119-124
%V 57
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2013-027-2/
%R 10.4153/CMB-2013-027-2
%F 10_4153_CMB_2013_027_2

[1] [1] Balcar, B., Dočkálková, J., and Simon, P., Almost disjoint families of countable sets. In: Finite and infinite sets, Vol. I, II (Eger, 1981), Colloq. Math. Soc. János Bolyai 37, North-Holland, Amsterdam, 1984, 59–88. Google Scholar

[2] [2] Balcar, B. and Simon, P., Disjoint refinement. In: Handbook of Boolean algebras, Vol. 2, North-Holland, Amsterdam, 1989, 333–388. Google Scholar

[3] [3] Erdős, P. and Shelah, S., Separability properties of almost-disjoint families of sets. Israel J. Math. 12 (1972), 207–214. Google Scholar | DOI

[4] [4] Kamburelis, A. and Węglorz, B., Splittings. Arch. Math. Logic 35 (1996), 263–277. Google Scholar | DOI

[5] [5] Raghavan, D. and Steprāns, J., On weakly tight families. Canad. J. Math., to appear. Google Scholar | DOI

[6] [6] Shelah, S., Mad families and sane player. Preprint, 0904.0816. Google Scholar

[7] [7] Simon, P., A note on almost disjoint refinement. In: 24thWinter School on Abstract Analysis (Benešova Hora, 1996), Acta Univ. Carolin. Math. Phys. 37 (1996), 89–99. Google Scholar

Cité par Sources :