We present and analyze the semantics and static type system for BeCecil, a theoretical (core) language with multimethods. BeCecil is a simple and orthogonal version of object-oriented languages like Cecil, CLOS, and Dylan. BeCecil has a new, simple mechanism for information hiding, which allows subclassing and yet can preserve representation invariants. BeCecil is also block-structured; within a block, one can extend a generic function with new multimethods, which may come from other generic functions. The inheritance relationships of objects may be extended in any block, and are statically scoped. The type system separates classes from types, and inheritance from subtyping. Subtype relationships are also extensible and statically scoped. These features combine to make BeCecil unusually expressive, while still allowing static typechecking.