Computable fields and arithmetically definable ordered fields

Computable Ordered Abelian Groups and Fields

We present transformations of linearly ordered sets into ordered abelian groups and ordered fields. We study effective properties of the transformations. In particular, we show that a linear order L has a ∆2 copy if and only if the corresponding ordered group (ordered field) has a computable copy. We apply these codings to study the effective categoricity of linear ordered groups and fields.

Definable Sets in Valued Fields

Ordered Rings and Fields

Computable Algebra, General Theory and Theory of Computable Fields(1)

Introduction. Abstract algebra is the product of a transition from such concrete systems as the ring of integers or the field of rational numbers to the corresponding, axiomatically defined, abstract systems. In the course of this abstraction process various properties of the concrete system are lost. The field of rational numbers, for example, possesses a natural topology, an ordering, and fur...

On Partly Ordered Fields