- Tytuł:
- Hausdorff ’s theorem for posets that satisfy the finite antichain property
- Autorzy:
-
Abraham, Uri
Bonnet, Robert - Powiązania:
- https://bibliotekanauki.pl/articles/1205278.pdf
- Data publikacji:
- 1999
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
ordinals
partial orderings
scattered partial orderings
Hausdorff's theorem - Opis:
-
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 - Źródło:
-
Fundamenta Mathematicae; 1999, 159, 1; 51-69
0016-2736 - Pojawia się w:
- Fundamenta Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł