Abstract: In this paper the auther begins with some known results about ηλ(=the least cardinal K such that K→（λ）~<∞), proving this theorem: If λ is not Ramsey cardinal and ηλ exists, then for every a<ηλ there is a weakly compact cardinal γ, such that λ<γα<ηλandγα<γβwhenever a<β<ηλ, therefore ηλ is the limit of the sequence（γα:a<ηλ）, i.e. ηλ=limγα. The theorem is mainly based on the theory of models with indiscernibles. 

Key words: indiscernibles, Ramsey cardinal, cardinal η₂