Thanks for the article, I read most of it and like much of it.
"For it would have been possible for Christ to do everything that the Holy Spirit was to carry out. But this is the reason why the Holy Spirit proceeds to miraculous deeds, so that we may learn of His importance. Similarly, the Father could have created all beings, but the Son does this so that we may learn of his power. It is for the same reason that the Holy Spirit undertakes such activity... For the Father is capable of doing all things, as is the Son and the Holy Spirit. (emphasis added) ......
This is the kind of co-equalness I can readily identify with. However, this does not seem to match my interpretation of what Kosta was saying about "causes".
"Is the Spirit greater than you (the Son) because that which could not be borne by the disciples he now prepares us to bear? Is his energy greater and more perfect? No, I am not saying this. For he will declare 'what is mine.' This is why it is said: 'For he will not speak on his own authority, but whatever he hears he will speak...' But because he said, 'He will teach and remind you . . .' and that 'he will guide you into all the truth,' he also said, 'He will take what is mine and declare it to you,' so that you will not assume that the Spirit is greater. This means that whatever I (Christ) have said to you, he (the Spirit) will also say to you . . . nothing contrary, except the same things that I have said. And as the Son said, 'I do not speak on my behalf,' meaning that he does not say anything that is his alone and does not come from the Father, so also with the Holy Spirit. The expression, 'He will take what is mine and declare it to you,' as far as I know, has to do with the knowledge of the Son. For the knowledge of the Son and of the Spirit is one and the same ...
This is another good example. None is greater than the others. I really didn't see anything in this article portraying the Father as either "greater" or even a first among equals in the general sense. That is, some see the Pope as a first among equals in a general sense. I didn't see Chrysostom making a similar case for the Father. But that IS the case I thought Kosta was making with "causes".