16 citations · 63 across the 23 of their papers we have counts for
26 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…
Vector spaces with a union of independent subspaces
Alessandro Berarducci, Marcello Mamino, Rosario Mennuni
Motivated by the theory of locally definable groups, we study the theory of -vector spaces with a predicate for the union of an infinite family of independent subspaces. We…
Is the twin prime conjecture independent of Peano Arithmetic?
Alessandro Berarducci, Antongiulio Fornasiero, Joel David Hamkins
We show that there is an arithmetical formula F such that ZF proves that F is independent of PA and yet, unlike other arithmetical independent statements, the truth value of F cann…
Provability Logic: models within models in Peano Arithmetic
Alessandro Berarducci, Marcello Mamino
In 1994 Jech gave a model theoretic proof of Gödel's second incompleteness theorem for Zermelo-Fraenkel set theory in the following form: ZF does not prove that ZF has a model. Kot…
On the value group of the transseries
Alessandro Berarducci, Pietro Freni
We prove that the value group of the field of transseries is isomorphic to the additive reduct of the field.