sentences:  Strong partition cardinal
  
  In Zermelo–Fraenkel set theory without the axiom of choice a strong partition cardinal is an uncountable well-ordered cardinal formula_1 such that every partition of the set formula_2of size formula_1 subsets of formula_1 into less than formula_1 pieces has a homogeneous set of size formula_1.The existence of strong partition cardinals contradicts the axiom of choice.