16 pitcher: interrelations of 



belonging to the class ^'"^ of the development A. The element r"' 

 is said to represent the class 'iP'"' and its elements p"*'. It is under- 

 stood however that only the existent classes 'ip™' have representative 

 elements r"'. 



14. Various classes derived from a development A* — For a de- 

 velopment A the class '^'": 



is the class of all elements (in notation: p"^) developed in the stage m, 

 the least common superclass of the classes of the stage m; and the 

 class *!l3*^ " 



^V = [p^] ^ UA = U(i^"")) ^ UC^]?-), 



is the class of all elements (in notation: p^) developed in the develop- 

 ment A, the least conunon superclass of the classes 'ip'"' of A. 

 The class ^l}"": 



is the class of all elements (in notation : p^") not developed in stage m, 

 and the class f'm'- 



•^^ = u(i^-'"»lmo ^ m), 



is the class of all elements each for some stage TOo ^ wt not developed, 

 the least common superclass of the classes ^]?~™'(mo ^ m). 



As to an element p the indices I of existent classes of stage m are 

 designated by the notations: 



g"; hp, 



according as the class 'ip'"' contains or does not contain the element p. 

 Then the class '^f"': 



is the least common superclass of the classes of stage m which contain 

 p, the class of all elements each of which is by stage m of the develop- 

 ment directly connected with the element p, in that they belong to the 

 same class of stage m. The class '^pm: 



^pm = u(^'^|mo ^ m), 



is the least common superclass of the classes ^""""(too ^ m), the class 

 of all elements each of which is by some stage mo ^ m of the develop- 

 ment directly connected with the element p. 

 * I. G. A., § 76. 



