In the present paper, we propose a new axiomatic approach to nonstandard analysis and its application general theory of spatial structures in terms category theory. Our framework is based on idea internal set theory, while make use an endofunctor U topos sets S together with natural transformation υ, instead as “standard”, “internal”, or “external”. Moreover, notion space called U-space, USpace...

Wedemonstrate that a comprehensive nonstandard set theory can be developed in the standard ∈-language. As an illustration, a nonstandard Law of Large Numbers is obtained.

BACKGROUND Empirical evidence has demonstrated adverse associations between parental nonstandard work schedules (i.e., evenings, nights, or weekends) and child developmental outcomes. However, there are mixed findings concerning the relationship between parental nonstandard employment and children’s body mass index (BMI), and few studies have incorporated information on paternal work schedules....

We propose a new model of computation based on Nonstandard Analysis. Intuitively, the role of ‘algorithm’ is played by a new notion of finite procedure, called Ω-invariance and inspired by physics, from Nonstandard Analysis. Moreover, the role of ‘proof’ is taken up by the Transfer Principle from Nonstandard Analysis. We obtain a number of results in Constructive Reverse Mathematics to illustra...

In this note, we make two nonstandard group-theoretic observations. First, we give a short nonstandard proof of a well-known result in group theory concerning locally nilpotent groups. Second, we outline a nonstandard way of viewing the projective limit of an projective family of groups. (We are unsure if this second observation, in some form, has already been discovered, although we would not ...

We present Nonstandard Analysis by three axioms: the Extension, Transfer and Saturation Principles in the framework of the superstructure of a given innnite set. We also present several applications of this axiomatic approach to point-set topology. Some of the topological topics such as the Hewitt realcompactiication and the nonstandard characterization of the sober spaces seem to be new in the...

We approach the study of differentiable manifolds modeled on Banach spaces by means of Nonstandard Analysis. We stay inside the category of classical manifolds and using nonstandard analysis techniques, we present some new nonstandard characterizations for the tangent bundle, differentiable function, differential of a function, directional derivatives, etc. We establish some relations between o...

We present Nonstandard Analysis by three axioms: the Extension, Transfer and Saturation Principles in the framework of the superstructure of a given innnite set. We also present several applications of this axiomatic approach to point-set topology. Some of the topological topics such as the Hewitt realcompactiication and the nonstandard characterization of the sober spaces seem to be new in the...

In 1963, Abraham Robinson applied his newly discovered nonstandard analysis to formal firstorder languages and developed a nonstandard logic [9] relative to the “truth” concept and structures. Since that time not a great deal of fundamental research has been attempted in this specific area with one notable exception [2]. However, when results from this discipline are utilized they have yielded ...