Published online by Cambridge University Press: 12 March 2014
In this paper, we shall state some results concerning ℵ0-complete cardinals and the transcendency of cardinals which is proposed by G. Takeuti [6]. The main purpose of this paper is to prove the following theorems.
Theorem 1. Let ℵ1, be the first ℵ0-complete cardinal number. Then the transcendency of cardinals holds for Δ11-functions of ℵ1-language.