Characterizing Internal and External Sets

Abstract

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.