Some structural similarities between uncountable sets, powersets and the universe

Similarities between powersets of terms 1

Generalisation of the foundational basis for many-valued logic programming builds upon generalised terms in form of powersets of terms. A categorical approach involving set and term functors as monads allows for a study of monad compositions that provide variable substitutions, and compositions thereof. In this paper, substitutions and unifiers appear as constructs in Kleisli categories related...

Cohesive Sets: Countable and Uncountable

We show that many uncountable admissible ordinals (including some cardinals) as well as all countable admissible ordinals have cohesive subsets. Exactly which cardinals have cohesive subsets, however, is shown to depend on set-theoretic assumptions such as V=L or a large cardinal axiom. The study of recursion theory on the ordinals was initiated by Takeuti and then generalized by several others...

The Structural Relationship Between Topological Indices and Some Thermodynamic Properties

The fact that the properties of a molecule are tightly connected to its structural  characteristics  is one of the fundamental concepts in chemistry. In this connection,  graph theory has been successfully applied in developing some relationships between topological indices and some thermodynamic properties. So ,  a novel method for computing the new descriptors to construct a quantitative rela...

Structural similarities of some secondary lead minerals

Some structural analogies found in tsumebite, vauquelinite, forns.cite, and brackebuschite make it possible to place these secondary lead minerMs in the s~me series with general formula Pb~MeII(Z)(XQ)(Y04), where MelI is a bivalent cation as Cu 2+ or Mn 2+, Z is the hydroxyl group or the w~ter molecule, X is S, Cr, or V, ~nd Y is P, As, or V. Some crystallochemical considerations are developed ...

From Finite to Uncountable Sets