Lindström theorems characterize logics in terms of model-theoretic conditions such as Compactness and the Löwenheim-Skolem property. Most existing characterizations of this kind concern extensions of first-order logic. But on the other hand, many logics relevant to computer science are fragments or extensions of fragments of first-order logic, e.g., k-variable logics and various modal logics. F...

Preservation theorems are amongst the earliest areas of study in classical model theory. One of the first preservation theorems to be proven is the Łoś-Tarski theorem that provides over arbitrary structures and for arbitrary finite vocabularies, semantic characterizations of the ∀ and ∃ prefix classes of first order logic (FO) sentences, via the properties of preservation under substructures an...

A self-contained electromagnetic theory is developed on a simplicial lattice. Instead of dealing with vectorial field, discrete exterior calculus (DEC) studies the discrete differential forms of electric and magnetic fields, and circumcenter dual is adopted to achieve diagonal Hodge star operators. In this paper, Gauss’ theorem and Stokes’ theorem are shown to be satisfied inherently within DEC...

In this paper, a self-contained electromagnetic theory is derived on a regular lattice. The discretized form of integral and diierential calculus, which is called`discrete calculus' here, is used to describe this theory. It is shown that discrete forms of Gauss' theorem, Stokes' theorem, Green's theorem, and Huygens' principle can be derived. Moreover, many electromagnetic theorems can also be ...

This paper is concerned with formalizations and veriications in type theory that are abstracted with respect to a large class of datatypes; i.e polytypic formalizations. The main advantage of these developments are that they can not only be used to polytypically deene functions but also to formally state polytypic theorems and to interactively develop polytypic proofs using existing proof edito...

We show in this article that the most usual finiteness conditions on a subgroup of a finitely generated group all have equivalent formulations in terms of formal language theory. This correspondence gives simple proofs of various theorems concerning intersections of subgroups and the preservation of finiteness conditions in a uniform manner. We then establish easily the theorems of Greibach and...

The main aim of this work is to introduce and study the notions generalized regularity, normality, symmetric in fuzzy soft topological spaces via closed sets. Investigating some their basic properties. Many related theorems relations these are presented. Moreover, hereditary property preservation discussed.

Correspondence: [email protected]. edu.cn Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P. R. China Abstract Galilean invariance for general conservative finite difference schemes is presented in this article. Two theorems have been obtained for firstand second-order conservative schemes, which demonstrate the necessity conditions for Galilean prese...

Diverse classes of fuzzy relations such as reflexive, irreflexive, symmetric, asymmetric, antisymmetric, connected, and transitive fuzzy relations are studied. Moreover, intersections of basic relation classes such as tolerances, tournaments, equivalences, and orders are regarded and the problem of preservation of these properties by n-ary operations is considered. Namely, with the use of fuzzy...