Research Article

MetaStructure, Meta-HyperStructure, and Meta-SuperHyper Structure

Abstract

This paper investigates new hierarchical frameworks in mathematics by extending the notion of classical structures. A Structure refers to an arbitrary mathematical framework, including but not limited to those from Set Theory, Logic, Probability, Statistics, Algebra, and Geometry. A HyperStructure generalizes classical algebraic structures by replacing the underlying set S with its powersetP(S), where hyperoperations combine subsets into (possibly new) subsets, enabling the expression of higher–order relations. A  uperHyperStructure further extends this idea by recursively applying the powerset construction, capturing increasingly complex hierarchical interactions. In addition, we introduce and study the concepts of MetaStructure, Iterated MetaStructure, Meta-HyperStructure, and Meta SuperHyperStructure. A MetaStructure treats entire mathematical structures as objects, with meta-operations producing new structures.
An Iterated MetaStructure arises by repeatedly applying the MetaStructure construction, thereby forming hierarchical layers where structures of structures yield progressively deeper meta-level frameworks. These approaches allow various mathematical and scientific concepts to be unified and generalized from a meta-level perspective, offering a systematic foundation for exploring higher-order structures across diverse fields.