Geodesic
Strongly almost disjoint familes, revisited
Fundamenta Mathematicae, Tome 163 (2000) no. 1, pp. 13-23

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

The relations M(κ,λ,μ) → B [resp. B(σ)] meaning that if $A⊂[κ]^λ$ with |A|=κ is μ-almost disjoint then A has property B [resp. has a σ-transversal] had been introduced and studied under GCH in [EH]. Our two main results here say the following: Assume GCH and let ϱ be any regular cardinal with a supercompact [resp. 2-huge] cardinal above ϱ. Then there is a ϱ-closed forcing P such that, in $V^P$, we have both GCH and $M(ϱ^{(+ϱ+1)},ϱ^+,ϱ) ↛ B$ [resp. $M(ϱ^{(+ϱ+1)},λ,ϱ) ↛ B(ϱ^+)$ for all $λ ≤ ϱ^{(+ϱ+1)}]$. These show that, consistently, the results of [EH] are sharp. The necessity of using large cardinals follows from the results of [Ko], [HJSh] and [BDJShSz].
DOI : 10.4064/fm-163-1-13-23
Keywords: strongly almost disjoint family, property B, σ-transversal

A. Hajnal 1 ; I. Juhász 1 ; S. Shelah 1

1 
@article{10_4064_fm_163_1_13_23,
     author = {A. Hajnal and I. Juh\'asz and S. Shelah},
     title = {Strongly almost disjoint familes, revisited},
     journal = {Fundamenta Mathematicae},
     pages = {13--23},
     publisher = {mathdoc},
     volume = {163},
     number = {1},
     year = {2000},
     doi = {10.4064/fm-163-1-13-23},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/fm-163-1-13-23/}
}
TY  - JOUR
AU  - A. Hajnal
AU  - I. Juhász
AU  - S. Shelah
TI  - Strongly almost disjoint familes, revisited
JO  - Fundamenta Mathematicae
PY  - 2000
SP  - 13
EP  - 23
VL  - 163
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/fm-163-1-13-23/
DO  - 10.4064/fm-163-1-13-23
LA  - en
ID  - 10_4064_fm_163_1_13_23
ER  - 
%0 Journal Article
%A A. Hajnal
%A I. Juhász
%A S. Shelah
%T Strongly almost disjoint familes, revisited
%J Fundamenta Mathematicae
%D 2000
%P 13-23
%V 163
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/fm-163-1-13-23/
%R 10.4064/fm-163-1-13-23
%G en
%F 10_4064_fm_163_1_13_23
A. Hajnal; I. Juhász; S. Shelah. Strongly almost disjoint familes, revisited. Fundamenta Mathematicae, Tome 163 (2000) no. 1, pp. 13-23. doi: 10.4064/fm-163-1-13-23

Cité par Sources :