On the existence of real-closed fields that are _{}-sets of power ℵ_{}

@article{Alling1962OnTE,
  title={On the existence of real-closed fields that are _\{\}-sets of power ℵ_\{\}},
  author={N. L. Alling},
  journal={Transactions of the American Mathematical Society},
  year={1962},
  volume={103},
  pages={341-352}
}
  • N. L. Alling
  • Published 1962
  • Mathematics
  • Transactions of the American Mathematical Society
Introduction. In the theory of 7la-sets three main theorems stand out: I. An 77-set is universal for totally ordered sets of power not exceeding Ka. II. Two 71a-sets of power R. are isomorphic. III. If R. is regular and if Ea 0 then these three theorems hold for the category of totally ordered Abelian groups and order preserving (group) isomorphisms; the special group being totally ordered, Abelian, divisible, and an 77a-set. Erdos, Gillman, and Henriksen [8] (see also Gillman and Jerison [11… Expand
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