The Elementary Theory of Dedekind Cuts

Contents 1. Introduction. 2. Heirs. 3. The invariance group of a cut. 4. Review of T-convex valuation rings. 5. The invariance valuation ring of a cut. 6. A method for producing cuts with given signature. 7. Existentially closed extensions. 8. The elementary theory of convex subgroups. 9. The elementary theory of cuts. 10. Counter examples. 1. Introduction. Let X be a totally ordered set. A (Dedekind) cut p of X is a tuple (p L ; p R) of subsets p L ; p R of X such that p L p R = X and p L < p R , i.e. a < b for all a 2 p L ; b 2 p R. In this article we do the model theoretic groundwork of the rst order