The Field of Reals with a Predicate for the Powers of Two.
The Joly–Becker theorem for –orderings
We prove the –version of the Joly–Becker theorem: a skew field admits a –ordering of level iff it admits a –ordering of level for some (resp. all) odd . For skew fields with an imaginary unit and fields stronger results are given: a skew field with imaginary unit that admits a –ordering of higher level also admits a –ordering of level . Every field that admits a –ordering of higher level admits a –ordering of level or
The limit behaviour of exponential terms
Topology on ordered fields
An ordered field is a field which has a linear order and the order topology by this order. For a subfield of an ordered field, we give characterizations for to be Dedekind-complete or Archimedean in terms of the order topology and the subspace topology on .
Two theorems on regularly r-closed fields.