we study different completeness definitions for two categories of lattice-valued cauchy spaces and the relations between these definitions. we also show the equivalence of a so-called completion axiom and the existence of a completion.

we investigate a class of fourth-order differential operators with eigenparameter dependent boundary conditions and transmission conditions. a self-adjoint linear operator a is defined in a suitable hilbert space h such that the eigenvalues of such a problem coincide with those of a . we discuss asymptotic behavior of its eigenvalues and completeness of its eigenfunctions. finally, we obtain th...

In mono-modal logic there is a fair number of high-powered results on completeness covering large classes of modal systems, witness for example Fine [74,85] and Sahlqvist [75]. Mono-modal logic is therefore a well-understood subject in contrast to poly-modal logic where even the most elementary questions concerning completeness, decidability etc. have been left unanswered. Given that so many ap...

The following case is interesting from the completeness of the history and the satisfactory termination. Mr. G., European, merchant by occupation, age thirty-eight years, consulted me in September of this year for severe pain in the back and left loin ; he gave me a gouty family history and in regard to his present trouble said that he had had a somewhat similar attack a year previously which h...

One of the key results in the eld of modularity for Term Rewriting Systems is the modularity of completeness for left linear TRSs established by Toyama Klop and Barendregt in TKB The proof however is quite long and involved In this paper a new proof of this basic result is given which is both short and easy employing the powerful technique of pile and delete already used with success in proving...

In this paper, we review two properties of completeness known as the Bourbaki-completeness and cofinal in setting metric spaces. These notions came from new classes generalized Cauchy sequences appearing when characterizing so-called Bourbaki-boundedness a similar way that characterize totally boundedness. For clustering Bourbaki–Cauchy cofinally sequences, have respectively what is call The to...