What is the meaning of 'is' in the context of the Trinity?

The Philosopher Gottlob Frege distinguishes between four different meaning behind the word 'is': 1) 'is' as in identity; Saul is Paul. 2) 'is' as in predicate; Paul is Christian. 3) 'is' as in subset; Paul is a Man. (Paul is a member of the class 'Men'). 4) 'is' as in existence; God is. As one not raised or well versed in the Christian faith, I would like to know, when Christians say "The Father is God. The Son is God. The Holy Spirit is God, and yet the Father is not the Son, the Son is not the Holy Spirit, the Holy spirit is not the Father." what meaning they ascribe to the word 'is'. Please feel free to give the different answers according to the different branches of Christianity. Addendum: If the answer is 1), identity, how do Christians get around the problem of the Transitivity of Identity' If A = B & B = C then A = C?