相关论文: Some applications of the ultrapower theorem to the…

This paper develops a categorical framework to clarify the relationship between the completeness and compactness theorems in classical first-order logic. Rather than claiming that different model constructions yield naturally isomorphic…

We pursue the study of Ultracategories initiated by Makkai and more recently Lurie by looking at properties of Ultracategories of complete metric structures, i.e. coming from continuous model theory, instead of ultracategories of models of…

A classical theorem of Hechler asserts that the structure $\left(\omega^\omega,\le^*\right)$ is universal in the sense that for any $\sigma$-directed poset P with no maximal element, there is a ccc forcing extension in which…

There exist two known canonical types of ultrafilter extensions of first-order models; one comes from modal logic and universal algebra, another one from model theory and algebra of ultrafilters, with ultrafilter extensions of semigroups as…

We use topological methods to study complexity of deep computations and limit computations. We use topology of function spaces, specifically, the classification Rosenthal compacta, to identify new complexity classes. We use the language of…

Given a collection of K\"ahler forms and a continuous weight on a compact complex manifold we show that it is possible to define natural new notions of extremal potentials and equilibrium measures which coincide with classical notions when…

In four-dimensional compactifications of the heterotic superstring theory the K\"ahler potential has a form which generically induces a superpotential mass term for Higgs particles once supersymmetry is broken at low energies. This…

The K-energy functional is extended to complexified K\"ahler classes, providing a variational approach to study the scalar curvature equation with B-field introduced by Schlitzer and Stoppa. The extended K-energy is convex along geodesics…

In the simplest compactification, we discuss the intermediate unification in M-theory on $S^1/Z_2$, and point out that we can push the eleven dimension Planck scale to the TeV range if the gauge coupling in the hidden sector is super weak,…

We introduce and study two new relations between function spaces over measure spaces of infinite measure, motivated by the question of establishing compactness. The first relation captures the uniform decay of function (quasi-)norms ``at…

We present the study of type II A flux vacua and their M-theory duals for compactification on a class of Calabi-Yau orientifolds. The Kaehler potential is derived from toroidal compactifications and the superpotential contains a…

For a new class of topological vector spaces, namely $\kappa $-normed spaces, and associated quasisemilinear topological preordered space is defined and investigated. This structure arise naturally from the consideration of a $\kappa…

We study compactness and L\"owenheim-Skolem properties of fragments of the class-sized logic $\mathcal{L}_{\infty \infty}$ and of class-sized versions of second-order and sort logics. In these fragments, certain combinations of infinitary…

Using a reconstruction theorem, we prove that the supersymmetry conditions for a certain class of flux backgrounds are equivalent with a tractable subsystem of relations on differential forms which encodes the full set of contraints arising…

Supplementing and expanding classical results, for compact spaces $K$ and $L$, $L$ metric, and their Banach spaces $\mathcal{C}(L)$ and $\mathcal{C}(K)$ of continuous real-valued functions, we provide several characterizations of the…

Every mathematical structure has an elementary extension to a pseudo-countable structure, one that is seen as countable inside a suitable class model of set theory, even though it may actually be uncountable. This observation, proved easily…

The concepts of a conditional set, a conditional inclusion relation and a conditional Cartesian product are introduced. The resulting conditional set theory is sufficiently rich in order to construct a conditional topology, a conditional…

We review some aspects of theories with compact extra dimensions. We consider the motivation and the theoretical basis of Large, Universal and Warped Extra Dimensions. We focus on those aspects that are potentially relevant in the…

In this paper we consider finite dimensional dynamical systems generated by a Lipschitz function. We prove a version of the Whitney's Extension Theorem on compact manifolds to obtain a version of the well-known Lambda Lemma for Lipschitz…

There are two main aims of the paper. The first one is to extend the criterion for the precompactness of sets in Banach function spaces to the setting of quasi-Banach function spaces. The second one is to extend the criterion for the…