Geodesic
Hausdorff ’s theorem for posets that satisfy the finite antichain property
Fundamenta Mathematicae, Tome 159 (1999) no. 1, pp. 51-69.

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

Hausdorff characterized the class of scattered linear orderings as the least family of linear orderings that includes the ordinals and is closed under ordinal summations and inversions. We formulate and prove a corresponding characterization of the class of scattered partial orderings that satisfy the finite antichain condition (FAC).  Consider the least class of partial orderings containing the class of well-founded orderings that satisfy the FAC and is closed under the following operations: (1) inversion, (2) lexicographic sum, and (3) augmentation (where $〈P, \preceq〉$ augments 〈P, ≤〉 iff $x \preceq y$ whenever x ≤ y). We show that this closure consists of all scattered posets satisfying the
DOI : 10.4064/fm-159-1-51-69
Keywords: ordinals, partial orderings, scattered partial orderings, Hausdorff's theorem

Uri Abraham 1 ; Robert Bonnet 1

1 
@article{10_4064_fm_159_1_51_69,
     author = {Uri Abraham and Robert Bonnet},
     title = {Hausdorff {\textquoteright}s theorem for posets that satisfy the finite antichain property},
     journal = {Fundamenta Mathematicae},
     pages = {51--69},
     publisher = {mathdoc},
     volume = {159},
     number = {1},
     year = {1999},
     doi = {10.4064/fm-159-1-51-69},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/fm-159-1-51-69/}
}
TY  - JOUR
AU  - Uri Abraham
AU  - Robert Bonnet
TI  - Hausdorff ’s theorem for posets that satisfy the finite antichain property
JO  - Fundamenta Mathematicae
PY  - 1999
SP  - 51
EP  - 69
VL  - 159
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/fm-159-1-51-69/
DO  - 10.4064/fm-159-1-51-69
LA  - en
ID  - 10_4064_fm_159_1_51_69
ER  - 
%0 Journal Article
%A Uri Abraham
%A Robert Bonnet
%T Hausdorff ’s theorem for posets that satisfy the finite antichain property
%J Fundamenta Mathematicae
%D 1999
%P 51-69
%V 159
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/fm-159-1-51-69/
%R 10.4064/fm-159-1-51-69
%G en
%F 10_4064_fm_159_1_51_69
Uri Abraham; Robert Bonnet. Hausdorff ’s theorem for posets that satisfy the finite antichain property. Fundamenta Mathematicae, Tome 159 (1999) no. 1, pp. 51-69. doi : 10.4064/fm-159-1-51-69. http://geodesic.mathdoc.fr/articles/10.4064/fm-159-1-51-69/

Cité par Sources :