Purpose: Since the beginning of the 2000 s, numerous domain, upper level, and top level ontologies have been developed. In order to represent a model of the reality they contain tens to several thousand concepts, properties and axioms. These are instantiated into huge collections of facts about the world. In this paper, we propose a General Ontology Theory which focuses on a general formal description of ontological concepts. Methodology: We capture the fundamental structures and principles that that apply to the the elements of top level and upper level ontologies, potentially addressing overarching functionalities such as identity, abstraction, aggregation, classification, inheritance, subsumption, instantiation, and their relationships. To this end we use mathematical set theory to synthesize definitions and axioms along with guidelines for their application. Findings: The O4Top Ontology Blueprint is a schema that provides a foundation for conceptual and meta-level modeling. It supports the formalization of structural hierarchies for classes, relationship types and attributes. From that we can derive how particulars of classes are related to the set of their elements. As a result we are able to formulate subsumption axioms for classes and relationship types. We also can derive the hierarchical ordering merely from the set of particulars and their attributes. Originality: We define a minimal set of ontological elements that is sufficient for conceptual modeling in general. This supports the streamlining of ontologies and their terminologies.