13 citations · 46 across the 21 of their papers we have counts for
16 papers · 1 filter
Reflections on Trusting Lean
Lorenzo Bresolin, Marcello Mamino
It is known, by works of Werner and Carneiro, that the type theory of Lean (and indeed of CIC plus a version of choice) is equiconsistent with ZFC plus "there are infinitely many s…
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…
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…
Orthogonal decomposition of definable groups
Alessandro Berarducci, Pantelis E. Eleftheriou, Marcello Mamino
Orthogonality in model theory captures the idea of absence of non-trivial interactions between definable sets. We introduce a somewhat opposite notion of cohesiveness, capturing th…
One Lie group to define them all
Annalisa Conversano, Marcello Mamino
We produce a connected real Lie group that, as a first order structure in the group language, interprets the real field expanded with a predicate for the integers. Moreover, the do…
Asymptotic analysis of Skolem's exponential functions
Alessandro Berarducci, Marcello Mamino
Skolem (1956) studied the germs at infinity of the smallest class of real valued functions on the positive real line containing the constant , the identity function , and suc…
Fundamental group in o-minimal structures with definable Skolem functions
Bruno Dinis, Mário J. Edmundo, Marcello Mamino
In this paper we work in an arbitrary o-minimal structure with definable Skolem functions and we prove that definably connected, locally definable manifolds are uniformly definably…
Submodular Functions and Valued Constraint Satisfaction Problems over Infinite Domains
Manuel Bodirsky, Marcello Mamino, Caterina Viola
Valued constraint satisfaction problems (VCSPs) are a large class of combinatorial optimisation problems. It is desirable to classify the computational complexity of VCSPs dependin…
On the o-minimal Hilbert's fifth problem
Mario J. Edmundo, Marcello Mamino, Luca Prelli +2
Let be an arbitrary o-minimal structure. Let be a definably compact definably connected abelian definable group of dimension . Here we compute the new the intr…
On definably proper maps
Mário Edmundo, Marcello Mamino, Luca Prelli
In this paper we work in o-minimal structures with definable Skolem functions and show that a continuous definable map between Hausdorff locally definably compact definable spaces…
Groups definable in two orthogonal sorts
Alessandro Berarducci, Marcello Mamino
This work can be thought as a contribution to the model theory of group extensions. We study the groups G which are interpretable in the disjoint union of two structures (seen as a…
Discrete subgroups of locally definable groups
Alessandro Berarducci, Mário Edmundo, Marcello Mamino
We work in the category of locally definable groups in an o-minimal expansion of a field. Eleftheriou and Peterzil conjectured that every definably generated abelian connected grou…
Splitting definably compact groups in o-minimal structures
Marcello Mamino
An argument of A.Borel shows that every compact connected Lie group is homeomorphic to the Cartesian product of its derived subgroup and a torus. We prove a parallel result for def…
On the homotopy type of definable groups in an o-minimal structure
A. Berarducci, M. Mamino
Given a definably compact group G in a saturated o-minimal structure, there is a canonical homomorphism from G to a compact real Lie group F(G). We establish a similar result for t…
Higher homotopy of groups definable in o-minimal structures
Alessandro Berarducci, Marcello Mamino, Margarita Otero
It is known that a definably compact group G is an extension of a compact Lie group L by a divisible torsion-free normal subgroup. We show that the o-minimal higher homotopy groups…
Arithmetic of Dedekind cuts of ordered Abelian groups
Antongiulio Fornasiero, Marcello Mamino
We study the set of Dedekind cuts over a linearly ordered Abelian group as a structure over the language (0,<,+,-). Moreover, we obtain a simple set of axioms for the universal par…