# positive cone

## Primary tabs

Defines:
pre-positive cone
Type of Math Object:
Definition
Major Section:
Reference
Groups audience:

## Mathematics Subject Classification

### Difference in definitions

Again we have difference in definition. I think you need to add a reference here. Your definition of positive cone is not for instance in agreement with the definition found in

"Real Algebraic Geometry" by Bochnak, Coste and Roy. Springer 1998.

In modern real algebra, as far as I know, we do not consider P \cup -P to be the entire field. Maybe like your definition of partially ordered rings, you have to add a reference here.

### Re: Difference in definitions

Check out Lectures on Formally Real Fields by Alexander Prestel, published by Springer in 1984. I will add the reference shortly...

The condition P \cup - P = F* basically renders the partial order linear. So the entire book deals with linearly ordered fields (and rings).