Related papers: Model theory and ultraproducts
We survey various attempts to transport the ultraproduct construction from the realm of model theory to that of general topology.
Ultraproducts are a well-known tool in the classical model theory of first-order logic. We explore their uses in the context of finite model theory.
We present an introduction to modern continuous model theory with an emphasis on its interactions with topics covered in this volume such as $C^*$-algebras and von Neumann algebras. The role of ultraproducts is highlighted and expositions…
In the present paper we prove the compactness theorem with respect to partial structures and quasi-truth, using the technique of ultraproducts. Partial structures and quasi-truth are two notions developed within the partial structures…
We present a description of saturation in small $x$ deep inelastic scattering from power counting in a top-down effective theory derived from QCD. A factorization formula isolates the universal physics of the nucleus at leading power in…
An ultraproduct can be a helpful organizing principle in presenting solutions of problems at many levels, as argued by Terence Tao. We apply it here to the solution of a calculus problem: every infinite sequence has a monotone infinite…
In this work we extend the concept of the Lipschitz saturation of an ideal defined in [5] to the context of modules in some different ways, and we prove they are generically equivalent.
We survey the model theoretic approach to a variety of ultrapower embedding problems in operator algebras.
We determine the proof-theoretic strength of the principle of countable saturation in the context of the systems for nonstandard arithmetic introduced in our earlier work.
Highly saturated models are a fundamental part of the model-theoretic machinery of nonstandard analysis. Of the two methods for producing them, ultrapowers constructed with the aid of $\kappa^+$-good ultrafilters seems by far the less…
Our aim was to generalize some theorems about the saturation of ultra-powers to reduced powers. Naturally, we deal via saturation for types consisting of atomic formulas. We succeed to generalize the theory of dense linear is maximal and so…
This paper has been withdrawn. With the advancement of statistical theory and computing power, data sets are providing a greater amount of insight into the problems of today. Statisticians have an ever increasing number of tools to attack…
This paper is based on lectures presented to mathematical physicists and attempts to provide an overview of the present status of the Standard Model, its experimental tests, phenomenological and experimental motivations for going beyond the…
This paper presents a novel possible worlds semantics, designed to elucidate the underpinnings of ultrafinitism. By constructing a careful modification of the well-known Kripke models for inuitionistic logic, we seek to extend our…
We study various conditions under which a unitary in an ultraproduct of matrices is conjugated to an ultraproduct of permutations.
The paper is devoted to construction of some closed inductive sequence of models of the generalized second-order Dedekind theory of real numbers with exponentially increasing powers. These models are not isomorphic whereas all models of the…
We begin the study of the consequences of the existence of certain infinite matrices. Our present application is to compactness of products of topological spaces.
The development of supergravity unified models and their implications for current and future experiments are discussed.
We survey the developments in the model theory of tracial von Neumann algebras that have taken place in the last fifteen years. We discuss the appropriate first-order language for axiomatizing this class as well as the subclass of II$_1$…
Theoretical and experimental motivations behind supergravity grand unified models are described. The basic ideas of supergravity, and the origin of the soft breaking terms are reviewed. Effects of GUT thresholds and predictions arising from…