Weak versions of the axiom of choice for families of finite sets Page 80 WEAK VERSIONS OF THE AXIOM OF CHOICE FOR FAMILIES OF FINITE SETS CARLOS H. MONTENEGRO UNIVERSIDAD DE LOS ANDES, BOGOTA, COLOMBIA Abstract. We consider two weakenings of the axiom of choice for collections of finite sets. The first RCn states that every infinite subest X has an infinite Y CX such that [Y] n has a choice function (ie/:[Y] n—> Y with f (x)€ x for all x£[y] n). The second Cn states that every infinite collection P of sets of size n, has an infinite
