The gap-two cardinal problem for uncountable languages

摘要

In this paper we prove some cases of the gap-2 cardinal transfer theorem for uncountable languages assuming the axiom of constructibility. Consider uncountable cardinals κ, λ, with λ regular, a first order language L with at least one unary predicate symbol U, with |L| < min{κ, λ}. Given an L-structure A = 〈A,U~A, . . .〉, where |A| = κ~(++) and |U~A| = κ, we find an L-structure B = 〈B,UB, . . .〉 such that B ≡ A, |B| = λ~(++) and |U~B| = λ.