3 citations · 3 across the 12 of their papers we have counts for
12 papers
Volume of Tubes and Concentration of Measure in Riemannian Geometry
S. L. Cacciatori, P. Ursino
We investigate the notion of concentration locus introduced in \cite{CacUrs22}, in the case of Riemann manifolds sequences and its relationship with the volume of tubes. After prov…
Macdonald formula, Ricci Curvature, and Concentration Locus for classical compact Lie groups
Sergio L. Cacciatori, Pietro Ursino
For Classical compact Lie groups, we use Macdonald's formula \cite{Ma} and Ricci curvature for analyzing a "concentration locus", which is a tool to detect where a sequence of metr…
Decidability and NP-completeness for some languages which extend Boolean Set Theory
Pietro Ursino
We prove the decidability for a class of languages which extend BST and NP-completeness for a subclass of them. The languages BST extended with unordered cartesian product, BST ext…
Decidability of the satisfiability problem for Boolean set theory with the unordered Cartesian product operator
Domenico Cantone, Pietro Ursino
The satisfiability problem for multilevel syllogistic extended with the Cartesian product operator (MLSC) is a long-standing open problem in computable set theory. For long, it was…
Hilbert's Tenth problem and NP-completeness of Boolean Syllogistic with unordered cartesian product
Domenico Cantone, Pietro Ursino
We relate the decidability problem for BS with unordered cartesian product with Hilbert's Tenth problem and prove that BS with unordered cartesian product is NP-complete.
A Tenth Hilbert Problem-like Result: The Decidability of MLS with Unordered Cartesian Product
Pietro Ursino
Using the technique of formative processes, I solve the decidability problem of MLS with unordered cartesian product in the positive. Moreover I give a pure combinatorial descripti…
Concentration of measure for classical Lie groups
S. L. Cacciatori, P. Ursino
We study concentration of measure in Lie group actions. We define the notion of concentration locus of a flag sequence of Lie groups. Some examples of infinite group action on an i…
Two Dichotomy Theorems
Domenico Cantone, Pietro Ursino
We introduce the Dichotomy Property, a new property of some languages in Set Computable Theory, in order to explore the expressivity of some languages which are extensions of MLS.…
Universal Minimal Flow in the Theory of Topological Groupoids
Riccardo Re, Pietro Ursino
In this paper we investigate some connections between Topological Dynamics, the theory of G-Principal Bundles, and the theory of Locally Trivial Groupoids.
A generalized small model property for languages which force the infinity
Pietro Ursino
This paper deals with formulas of set theory which force the infinity. For such formulas, we provide a technique to infer satisfiability from a finite assignment.
Formative processes with applications to the decision problem in set theory: II. powerset and singleton operators, finiteness predicate
Domenico Cantone, Pietro Ursino
In this paper we solve the satisfiability problem of an extended fragment of set computable theory which "forces the infinity" by a fruitful use of the witness small model property…
Comparing the automorphism group of the measure algebra with some groups related to the infinite permutation group of the natural numbers
Pietro Ursino
We prove, by a straight construction, that the automorphism group of the measure algebra and the subgroup of the measure preserving ones cannot be isomorphic to the trivial automor…