Related papers: Nonstandard Universes
In this paper, we introduce a mathematical structure called Euclidean Universe. This structure provides a basic framework for Non-Archimedean Mathematics and in particular for Nonstandard Analysis.
Under consideration are the construction and properties of some special class of second other tangent sets on using the technique of nonstandard analysis.
These notes give an elementary approach to parts of the theory of standard Borel and analytic spaces.
We present Nonstandard Analysis by three axioms: the {\em Extension, Transfer and Saturation Principles} in the framework of the superstructure of a given infinite set. We also present several applications of this axiomatic approach to…
This review aims to provide a very short and pedestrian introduction to some of the basics of extra-dimensional physics. The hope is to facilitate access and to be, in some respects, complementary to the many already existing reviews on…
This is a non-standard paper, containing some problems in set theory I have in various degrees been interested in. Sometimes with a discussion on what I have to say; sometimes, of what makes them interesting to me, sometimes the problems…
In this monograph, nonstandard characteristics for many notions from real analysis are obtained and applied. However, only two simple types of atomic formula are used and almost all of the characteristics are shown to hold for a simple…
The aim of this thesis is to question some of the basic assumptions that go into building the $\Lambda$CDM model of our universe. The assumptions we focus on are the initial conditions of the universe, the fundamental forces in the universe…
There has been significant recent progress in observational cosmology. This, in turn, has provided an unprecedented picture of the early universe and its evolution. In this review I will present a (biased) view of how one can use these…
The aim of this paper is to highlight a hitherto unknown computational aspect of Nonstandard Analysis. Recently, a number of nonstandard versions of Goedel's system T have been introduced ([2,9,12]), and it was shown in [26] that the…
The Standard Model of Particle Physics has been verified to unprecedented precision in the last few decades. However there are still phenomena in nature which cannot be explained, and as such new theories will be required. Since terrestrial…
We describe the non-minimal Standard Model, consisting of minimalistic extensions of the Standard Model, which for all we know is the theory of the universe, able to describe all of the universe from the beginning of time. Extensions…
A brief sketch is made of the present observational status of neutrino physics, with emphasis on the hints that follow from solar and atmospheric neutrino observations, as well as cosmological data on the amplitude of primordial density…
By presenting the proofs of a few sample results, we introduce the reader to the use of nonstandard analysis in aspects of combinatorics of numbers.
These lecture notes, to be completed in a later version, offer a short and rigorous introduction to Nostandard Analysis, mainly aimed to reach to a presentation of the basics of Loeb integration, and in particular, Loeb measures. The…
In section 1 of this paper, we characterize the isomorphism property of nonstandard universes in terms of the realization of some second--order types in model theory. In section 2, several applications are given. One of the applications…
These lecture notes provide an introduction to the theory and application of symmetry methods for ordinary differential equations, building on minimal prerequisites. Their primary purpose is to enable a quick and self-contained approach for…
A brief, non-technical review is given of certain defect-like configurations in the electroweak standard model, which may have played an important role in the physics of the early universe.
In this concise, albeit subjective review of structure formation, I shall introduce the cosmological standard model and its theoretical and observational underpinnings. I will focus on recent results and current issues in theoretical…
Short nonstandard proofs are given for some results about infinite systems of equations in infinitely many variables.