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In recursion theory, creative sets form a sharply distinguished subclass of the class of all recursively enumerable sets inasmuch as they own the greatest undecidability degree with respect to all algorithmic reducibilities studied in the theory. Other definitions of the various important classes of recursively enumerable sets axe presumably obtained via denying certain particular properties shared by creative sets. Thus, recall that the concept of a simple set S includes the idea of negating the existence of infinite recursively enumerable sets in the complement of S. It is a simple matter to prove that in the complements of creative sets, infinite recursively enumerable sets do exist. Of course, this is true not only for creative sets.That is the reason of why it seems interesting to seek for new properties which will contribute to gettin 8 a fuller characterization of creative sets. In this article, we make an attempt to find them. The property specified below makes use of the notion of a table. Note that other important classes of recursively enumerable sets, for instance, hyper-hypersimple sets, are also defined by means of tables.Throughout , all sets considered axe subsets of the set of natural numbers N. If A is a set, A is its complement; ~ is the empty set. Denote by {W~>0 the principal computable numeration of all recuzsively enumerable sets, and by {~oi}i>0 the principal computable numeration of all unary partial recursive functions; W~ is a recursively ennmerable set with number i and ~o~ is a partial recursive function with number i; W~ t and ~o~ axe finite parts of the set Wi and the function ~oj, respectively, computed after t steps in some fixed uniform enumeration of all W~ and ~oj. Write {Di)~>0 for the canonical numberin 8 of all finite sets. The Kantor numberin 8 functions axe denoted by c(z, ~/), l(z), and r(z).We need to adopt the requirement concernin 8 the enumeration, without repetition, of some recursively enumerable set T constructed by steps, which reads: an enumeration, without repetition, of the finite set T "+1 is an extension of the enumeration of T ~ As usual, AUB and Af3B axe the union and the intersection of sets A and B. A direct product of A and B is the set Ax B = {c (a, b)[a G A &c b E B} and a separable join is the set A(~B = {2fLirt E A}U{2r~-t-lln G B~.Write A