title: Supertransitive class
text: # Supertransitive class
  
  In set theory, a supertransitive class is a transitive class which includes as a subset the power set of each of its elements.
  
  Formally, let A be a transitive class. Then A is supertransitive if and only if
  
      $(\forall x)(x\in A\to {\mathcal {P}}(x)\subseteq A).$
  
  Here P(x) denotes the power set of x.
  
  