Marcus Tressl

The uniform companion for large differential fields of characteristic 0

We show that there is a theory UC of differential fields (in several commuting derivatives) of characteristic

Axiomatization of local-global principles for pp-formulas in spaces of orderings

0

Comparison of exponential‐logarithmic and logarithmic‐exponential series

, which serves as a model companion for every theory of large and differential fields extending a model complete theory of pure fields. As an application, we introduce differentially closed ordered fields, differentially closed p-adic fields and differentially closed pseudo-finite fields.

Pseudo completions and completions in stages of o-minimal structures

Abstract.We use a model theoretic approach to investigate properties of local-global principles for positive primitive formulas in spaces of orderings, such as the existence of bounds and the axiomatizability of local-global principles. As a consequence we obtain various classes of special groups satisfying local-global principles for all positive primitive formulas, and we show that local-global principles are preserved by some natural constructions in special groups.

Computation of the z-radical in C(X)

We explain how the field of logarithmic-exponential series constructed in 20 and 21 embeds as an exponential field in any field of exponential-logarithmic series constructed in 9, 6, and 13. On the other hand, we explain why no field of exponential-logarithmic series embeds in the field of logarithmic-exponential series. This clarifies why the two constructions are intrinsically different, in the sense that they produce non-isomorphic models of Th; the elementary theory of the ordered field of real numbers, with the exponential function and restricted analytic functions.

The elementary theory of Dedekind cuts in polynomially bounded structures

For an o-minimal expansion R of a real closed field and a set

Model completeness of o-minimal structures expanded by Dedekind cuts

\fancyscript{V}

Bounded super real closed rings

of Th(R)-convex valuation rings, we construct a “pseudo completion” with respect to