DEFINITION A relational query language Q is BP-complete if for each relational database D, the set of all relations defined by the queries of Q on D is equal to the set of all first-order definable relations over D. More formally, fix some infinite universe U of atomic data elements. A relational database schema S is a finite set of relation names, each with an associated arity. A relational da...

This is an exposition of Lambek’s strengthening and generalization of the deduction theorem in categories related to intuitionistic propositional logic. Essential notions of category theory are introduced so as to yield a simple reformulation of Lambek’s Functional Completeness Theorem, from which its main consequences can be readily drawn. The connections of the theoremwith combinatory logic, ...

We investigate the question whether semi-completeness, i.e., weak termination plus connuence, of term rewriting systems is preserved under the normalization of right-hand sides. We give a simple counterexample showing that in general this transformation neither preserves weak termination nor (local) connuence. Moreover we present two conditions which are suucient for the preservation of semi-co...

Bimodal provability logic GLB, introduced by G. Japaridze, currently plays an important role in the applications of provability logic to proof-theoretic analysis. Its topological semantics interprets diamond modalities as derived set operators on a bi-scattered bitopological space. We study the question of completeness of this logic w.r.t. the most natural space of this kind, that is, w.r.t. an...

Baumslag conjectured in the 1970s that the automorphism tower of a finitely generated free group (free nilpotent group) must be very short. Dyer and Formanek [9] justified the conjecture concerning finitely generated free groups in the “sharpest sense” by proving that the automorphism group Aut(Fn) of a non-abelian free group Fn of finite rank n is complete. Recall that a group G is said to be ...

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...

We elaborate a recursive-theoretic method to define real numbers which are random to any jump of the halting problem. This is obtained by generalizing a result of V. Becher and G. Chaitin dealing with the class of cofinite sets. As in the work of V. Becher and S. Grigorieff (but this time in the context of open sets in Cantor space) appeal to completeness phenomena replaces machine arguments. M...

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...