Semantic completeness and syntax completeness are important characters of the general formal systems, two the completeness have different meaning for a formal system. This paper analyze the relation between semantic completeness of a formal system S and syntax completeness under certain condition and the relation between the syntax completeness of S and the syntax completeness of consistent ext...

here, a finsler manifold $(m,f)$ is considered with corresponding curvature tensor, regarded as $2$-forms on the bundle of non-zero tangent vectors. certain subspaces of the tangent spaces of $m$ determined by the curvature are introduced and called $k$-nullity foliations of the curvature operator. it is shown that if the dimension of foliation is constant, then the distribution is involutive a...

The intersection ideal graph Γ(S) of a semigroup S is simple undirected whose vertices are all nontrivial left ideals and two distinct I, J adjacent if only their nontrivial. In this paper, we investigate the connectedness Γ(S). We show that connected, then diameter at most two. Further, classify semigroups in terms such obtain domination number, independence girth strong metric dimension have ...

Here, a Finsler manifold $(M,F)$ is considered with corresponding curvature tensor, regarded as $2$-forms on the bundle of non-zero tangent vectors. Certain subspaces of the tangent spaces of $M$ determined by the curvature are introduced and called $k$-nullity foliations of the curvature operator. It is shown that if the dimension of foliation is constant, then the distribution is involutive...