In his monograph On Numbers and Games, JH Conway introduced a real-closed field
containing the reals and the ordinals as well as a great many less familiar numbers …

In 2001, the algebraico-tree-theoretic simplicity hierarchical structure of JH Conway's
ordered field of surreal numbers was brought to the fore by the first author and employed to …

Each surreal number has a unique Conway name (or normal form) that is characteristic of its
individual properties. The paper answers the following two questions that are naturally …

Berarducci (2000) studied irreducible elements of the ring k ((G< 0))⊕ Z, which is an integer
part of the power series field k ((G)) where G is an ordered divisible abelian group and k is …

Let k be a field and G a totally ordered abelian group. Let K= k ((G)) be the field of
generalised power series with coefficients in k and exponents in G equipped with the …

Conway's field No of surreal numbers comes both with a natural total order and an
additional" simplicity relation" which is also a partial order. Considering No as a doubly …

We study necessary and sufficient conditions for a valued field K with value group G and
residue field k (with char K= chark) to admit a truncation closed embedding in the field of …

Real closed fields, and structures associated with them, are interesting from the point of view
of both model theory and computability. In this paper, we give results on the complexity of …

Let k be a field and Γ an (additive) ordered1 abelian group. Then we have the Hahn field K:=
k ((tΓ)) whose elements are the formal series a=∑ γ aγtγ with coefficients aγ∈ k and …

We investigate valued fields which admit a valuation basis. Given a countable ordered
abelian group G and a real closed or algebraically closed field F with subfield K, we give a …