4 citations · 7 across the 8 of their papers we have counts for
9 papers
A Euclidean comparison theory for the size of sets
Marco Forti
We discuss two main ways in comparing and evaluating the size of sets: the "Cantorian" way, grounded on the so called Hume principle (two sets have equal size if they are equipoten…
Euclidean integers, Euclidean ultrafilters, and Euclidean numerosities
Mauro Di Nasso, Marco Forti
We introduce axiomatically the ring of the Euclidean integers, that can be viewed as the ``integral part" of the field of Euclidean numbers of [4], where th…
A topological interpretation of three Leibnizian principles within the functional extensions
Marco Forti
Three philosophical principles are often quoted in connection with Leibniz: "objects sharing the same properties are the same object" (Identity of indiscernibles), "everything can…
The Euclidean numbers
Vieri Benci, Marco Forti
We introduce axiomatically a Nonarchimedean field E, called the field of the Euclidean numbers, where a transfinite sum is defined that is indicized by ordinal numbers less than th…
Natural numerosities of sets of tuples
Marco Forti, Giuseppe Morana Roccasalvo
We consider a notion of "numerosity" for sets of tuples of natural numbers, that satisfies the five common notions of Euclid's Elements, so it can agree with cardinality only for f…
A simple algebraic characterization of nonstandard extensions
Marco Forti
We introduce the notion of "functional extension" of a set X, by means of two natural algebraic properties of the operator * on unary functions. We study the connections with ultra…
Leibniz's Principles and Topological Extensions
Marco Forti
Three philosophical principles are often quoted in connection with Leibniz: "objects sharing the same properties are the same object", "everything can possibly exist, unless it yie…
Quasi-selective and weakly Ramsey ultrafilters
Marco Forti
Selective ultrafilters are characterized by many equivalent properties, in particular the Ramsey property that every finite colouring of unordered pairs of integers has a homogeneo…
Quasi-selective ultrafilters and asymptotic numerosities
Andreas Blass, Mauro Di Nasso, Marco Forti
We isolate a new class of ultrafilters on N, called "quasi-selective" because they are intermediate between selective ultrafilters and P-points. (Under the Continuum Hypothesis the…