  The notion of subtyping has gained an important role both in theoretical and
applicative domains: in lambda and concurrent calculi as well as in programming
languages. The soundness and the completeness, together referred to as the
preciseness of subtyping, can be considered from two different points of view:
operational and denotational. The former preciseness has been recently
developed with respect to type safety, i.e. the safe replacement of a term of a
smaller type when a term of a bigger type is expected. The latter preciseness
is based on the denotation of a type which is a mathematical object that
describes the meaning of the type in accordance with the denotations of other
expressions from the language. The result of this paper is the operational and
denotational preciseness of the subtyping for a synchronous multiparty session
calculus. The novelty of this paper is the introduction of characteristic
global types to prove the operational completeness.
