Article Dans Une Revue Fundamenta Mathematicae Année : 1996

Monotone sigma-complete groups with unbounded refinement

Résumé

The real line R may be characterized as the unique nonatomic directed partially ordered abelian group which is monotone sigma-complete (countable increasing bounded sequences have suprema), satisfies the countable refinement property (countable sums $\sum_ma_m=\sum_nb_n$ of positive elements $a_m$, $b_n$ have common refinements) and that is linearly ordered. We prove here that the latter condition is not redundant, thus solving an old problem by A. Tarski, by proving that there are many spaces (in particular, of arbitrarily large cardinality) satisfying all above listed axioms except linear ordering.

Fichier principal
Vignette du fichier
nontrivSCA.pdf (148.8 Ko) Télécharger le fichier

Dates et versions

hal-00004375 , version 1 (06-03-2005)

Licence

Identifiants

  • HAL Id : hal-00004375 , version 1

Citer

Friedrich Wehrung. Monotone sigma-complete groups with unbounded refinement. Fundamenta Mathematicae, 1996, 151, pp.177-187. ⟨hal-00004375⟩
155 Consultations
148 Téléchargements

Partager

  • More