Characterizing Internal and External Sets

The aim of this paper is to give a characterization between the external and internal sets, and some relation between the galaxies and monads, according to this paper we obtain the following results : A set is galaxy iff there exists a strictly increasing sequence of internal sets such that .Also A set is monad iff there exists a strictly decreasing sequence of internal sets such that . If is a galaxy and is a monad such that , then there exists an internal set such that . A monad is not galaxy. If is a monad and is a galaxy, the set of all internal functions such that is a monad)Keywords: Galaxy, Monad , Internal, External.