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.

Nominalistic Logic (NL) is a new presentation of Paul Gilmore’s Intensional Type Theory (ITT) as a sequent calculus together with a succinct nominalization axiom (N) that permits names of predicates as individuals in certain cases. The logic has a flexible comprehension axiom, but no extensionality axiom and no infinity axiom, although axiom N is the key to the derivation of Peano’s postulates ...

Health insecurity has emerged as a major concern among health policy-makers particularly in low- and middle-income countries (LMICs). It includes the inability to secure adequate healthcare today and the risk of being unable to do so in the future as well as impoverishing healthcare expenditure. The increasing health insecurity among 150 million of the world's poor has moved social protection i...

Veblen has given a set of axioms for geometry.!. The first eight of these are as follows : % Axiom I. There exist at least two distinct points. Axiom II. If points A, B, C are in the order ABC, they are in the order CBA. Axiom III. If points A, B, C are in the order ABC, they are not in the order BCA. Axiom IV. If points A, B, C are in the order ABC, then A is distinct from C. Axiom V. If A and...