we present some model theoretic results for {l}ukasiewiczpredicate logic by using the methods of continuous model theorydeveloped by chang and keisler.we prove compactness theorem with respect to the class of allstructures taking values in the {l}ukasiewicz $texttt{bl}$-algebra.we also prove some appropriate preservation theorems concerning universal and inductive theories.finally, skolemizatio...

In this paper we show that the compactness of a Loeb space depends on its cardinality, the nonstandard universe it belongs to and the underlying model of set theory we live in. In §1 we prove that Loeb spaces are compact under various assumptions, and in §2 we prove that Loeb spaces are not compact under various other assumptions. The results in §1 and §2 give a quite complete answer to a quest...

This paper is concerned with emptyness of the essential spectrum, or equivalently compactness of the semigroup, for perturbations of selfadjoint operators that are bounded below (on an L2-space). For perturbations by a (nonnegative) potential we obtain a simple criterion for compactness of the semigroup in terms of relative compactness of the operators of multiplication with characteristic func...

In an L-topological space we present good definitions for local compactness, weak local compactness and relative local compactness. We obtain the equivalence of these properties in a Hausdorff space and we also obtain a one point compactification theorem.

s: Amirali Abdullah Embedding results and lower bounds for Bregman divergences The Bregman divergences are a broad class of distance measures having high relevance in information theory, statistics and machine learning applications, and which include the Kullback-Leibler and Euclidean distance as special cases. The algorithmic tractability of these spaces is tightly linked with the underlying g...