5 citations · 14 across the 15 of their papers we have counts for
15 papers
Products of pseudofinite structures
Paola D'Aquino, Angus Macintyre
We prove that any product of a family of pseudofinite structures is pseudofinite. The main tools are the fundamental results on products of first order structures due to Feferman a…
Commutative unital rings elementarily equivalent to prescribed product rings
Paola D'Aquino, Angus Macintyre
The classical work of Feferman Vaught gives a powerful, constructive analysis of definability in (generalized) product structures, and certain associated enriched Boolean structure…
E-ideals in exponential polynomial ring
P. D'Aquino, A. Fornasiero, G. Terzo
We investigate exponential ideals within the context of exponential polynomial rings over exponential fields. We establish two distinct notions of maximality for exponential ideals…
The model theory of residue rings of models of Peano Arithmetic: The prime power case
P. D'Aquino, A. Macintyre
In \cite{MacResField} the second author gave a systematic analysis of definability and decidability for rings , where is a model of Peano Arith…
Some model-theoretic perspectives on the structure sheaves of Z hat and the ring of finite adèles over Q
Paola D'Aquino, Angus J. Macintyre, Margarita Otero
We use the classical Ax-Kochen-Ershov analysis of the model theory of Henselian fields to bring out some model-theoretical aspects of the structure sheaf of the spectrum of Z^ and…
Truncations of Ordered Abelian Groups
Paola D'Aquino, Jamshid Derakhshan, Angus Macintyre
The abstract will be added in due course.
A weak version of the Strong Exponential Closure
Paola D'Aquino, Antongiulio Fornasiero, Giuseppina Terzo
Assuming Schanuel's Conjecture we prove that for any variety V over the algebraic closure over the rational numbers, of dimension n and with dominant projections, there exists a ge…
A Theorem of Legendre in
Michele Bovenzi, Paola D'Aquino
We prove a classical theorem due to Legendre, about the existence of non trivial solutions of quadratic diophantine equations of the form , in the weak fragment o…
Comparing C and Zilber exponential fields, zero sets of exponential polynomials
Paola D Aquino, Angus Macintyre, Giuseppina Terzo
We continue the research programme of comparing the complex exponential field with Zilber exponential. For the latter we prove, using diophantine geometry, various properties about…
A valuation theoretic characterization of recursively saturated real closed fields
Paola D'Aquino, Salma Kuhlmann, Karen Lange
We give a valuation theoretic characterization for a real closed field to be recursively saturated. Our result extends the characterization of Harnik and Ressayre \cite{hr} for a d…
From Schanuel's Conjecture to Shapiro's Conjecture
P. D'Aquino, A. Macintyre, G. Terzo
In this paper we prove Shapiro's 1958 Conjecture on exponential polynomials, assuming Schanuel's Conjecture.
A theorem of complete reducibility for exponential polynomials
P. D'Aquino, G. Terzo
In this paper we give a factorization theorem for the ring of exponential polynomials in many variables over an algebraically closed field of characteristic 0 with an exponentiatio…
On the Value Group of a Model of Peano Arithmetic
Merlin Carl, Paola D'Aquino, Salma Kuhlmann
We investigate - real closed fields, that is, real closed fields which admit an integer part whose non-negative cone is a model of Peano Arithmetic. We show that the value gr…
Real closed exponential fields
Paola D'Aquino, Julia F. Knight, Salma Kuhlmann +1
In an extended abstract Ressayre considered real closed exponential fields and integer parts that respect the exponential function. He outlined a proof that every real closed expon…
A note on -saturated o-minimal expansions of real closed fields
Paola D'Aquino, Salma Kuhlmann
We give necessary and sufficient conditions for a polynomially bounded o-minimal expansion of a real closed field (in a language of arbitrary cardinality) to be -saturate…