Many concepts in object-oriented conceptual modelling have complex semantics that are unfortunately not precisely defined. This paper demonstrates that with a few simple and formally defined concepts one can define more complex concepts such as e.g. aggregation in a precise and formal way. The core concepts offer the possibility of layering modelling concepts: a particular pattern of simple lower level concepts can be used to represent a single high level concept. The advantage is that the high level concept is defined in terms of the lower level concepts. Because of their simplicity, the lower level concepts are much easier to define formally. The high-level concept benefits from this formal definition: its own formal definition can be inferred from the formal definition of its constituent lower level concepts. This layered approach can also be followed on a project by project basis by defining high-level concepts only applicable in the context of one particular project.