| Résume | Certain non-commutative ordered groups coming from o-minimal geometry (groups of definable unary germs) or real differential algebra (groups of transseries under composition) share important first-order properties. In order to find a tame first-order theory of extensions of such groups, it is necessary to understand their pure algebra.
To that end, valuation theoretic-like tools are particularly useful. In analogy with the valuation theory of fields, it is possible to develop an abstract theory of groups non-commutative formal series, equipped with a non-topological notion of infinite linearly ordered product. I will present a formalism for working with groups equipped with infinite products, describe their basic properties, and give prominent examples of such structures. |
