The notion of iteratively defined functions from and to heterogeneous term algebras is introduced as the solution of a finite set of equations of a special shape. Such a notion has remarkableâ€¦ (More)

PA is Peano arithmetic. The formula InterppA(r,/l) is a formalization of the assertion that the theory PA + a interprets the theory PA + , O (the variables a and are intended to range over codes ofâ€¦ (More)

Given an o-minimal structure M which expands a field, we define, for each positive integer d, a real valued additive measure on a Boolean algebra of subsets of Md and we prove that all the definableâ€¦ (More)

Let M be an o-minimal expansion of an ordered field. Let Ï† be a formula in the language of ordered domains. In this note we establish some topological properties which are transferred from Ï† to Ï† andâ€¦ (More)

We prove that if G is a group definable in a saturated o-minimal structure, then G has no infinite descending chain of type-definable subgroups of bounded index. Equivalently, G has a smallestâ€¦ (More)

The field of generalized power series with real coefficients and exponents in an ordered abelian divisible group G is a classical tool in the study of real closed fields. We prove the existence ofâ€¦ (More)

Berarducci, A. and B. Intrigila, Combinatorial principles in elementary number theory, Annals of Pure and Applied Logic 55 (1991) 35-50. We prove that the theory IA,, extended by a weak version ofâ€¦ (More)