Set-like equivalence and inner and outer cuts
Shiftings of the horizon
Some applications of non-standard analysis to proximity spaces
Some automorphisms of natural numbers in the alternative set theory
Some connections between measure, indiscernibility and representation of cuts
Some remarks to the axiom of prolongation
Spherical completeness with infinitesimals.
In the theory of nonarchimedean normed spaces over valued fields other than R or C, the property of spherical completeness is of utmost importance in several contexts, and it appears to play the role conventional completeness does in some topics of classical functional analysis. In this note we give various characterizations of spherical completeness for general ultrametric spaces, related to but different from the notions of pseudo-convergent sequence and pseudo-limit introduced by Ostrowski in...
Statistical Solutions of PDEs by Nonstandard Densities.
Strong initial segments of models of IΔ₀
McAloon showed that if 𝓐 is a nonstandard model of IΔ₀, then some initial segment of 𝓐 is a nonstandard model of PA. Sommer and D'Aquino characterized, in terms of the Wainer functions, the elements that can belong to such an initial segment. The characterization used work of Ketonen and Solovay, and Paris. Here we give conditions on a model 𝓐 of IΔ₀ guaranteeing that there is an n-elementary initial segment that is a nonstandard model of PA. We also characterize the elements that can be included....
Sull'ordinamento dei numeri reali non-standard
Several order-theoretic properties of the real axis, of the monads and of the infinites in nonstandard models of Analysis are considered. Pseudometrizability and topological completeness of related uniformities are studied.
Sur l'équation aux différences affine du premier ordre unidimensionnelle
On étudie les phénomènes de retard à la bifurcation et de butée pour des systèmes discrets lents-rapides du plan. On donne une explication géométrique de ces phénomènes basée sur l’examen de fonctions reliefs. On démontre ensuite l’existence et la vie brève des longs canards, qui sont des trajectoires ne présentant pas de butée. Trois exemples illustrent ces phénomènes. Le premier expose la problématique, le second permet une expérimentation de l’étude théorique sur les longs canards, le troisième...
Sur une classe d'algèbre de fonctions généralisées application aux systèmes différentiels