1 citations · 1 across the 2 of their papers we have counts for
6 papers
On the elementary theory of the real exponential field
Alessandro Berarducci, Francesco Gallinaro
Assuming Schanuel's conjecture, we prove that the complete theory of the real exponential field is axiomatized by the axioms of definably complete exponential fields sat…
Projective curves and weak second-order logic
Alessandro Berarducci, Francesco Gallinaro
Given an algebraically closed field of characteristic zero, we study the incidence relation between points and irreducible projective curves, or more precisely the poset of irr…
The Fundamental theorem of tropical differential algebra over nontrivially valued fields and the radius of convergence of nonarchimedean differential equations
Francesco Gallinaro, Stefano Mereta
We prove a fundamental theorem for tropical partial differential equations, analogous to the fundamental theorem of tropical geometry in this context. We extend results from Aroca…
Automorphisms of valued fields: amalgamation and existential closedness
Jan Dobrowolski, Francesco Gallinaro, Rosario Mennuni
We study valued fields equipped with an automorphism. We prove that all of them have an extension admitting an equivariant cross-section of the valuation. In residual characteristi…
Likely intersections in powers of the multiplicative group
Gabriel Andreas Dill, Francesco Gallinaro
We derive two finiteness properties as consequences of the geometrical non-degeneracy of an algebraic subvariety of a power of the multiplicative group, concerning the intersec…
Exponential sums equations and the Exponential Closedness conjecture
Vahagn Aslanyan, Francesco Gallinaro
This is an expository paper aiming to introduce Zilber's Exponential Closedness conjecture to a general audience. Exponential Closedness predicts when (systems of) equations involv…