HSP theorem

I have recently learned about the existence of Birkhoff's HSP theorem. A Google search gives me little insight into it. Could you please tell me where I could find any kind of deeper info? Is the proof very difficult to understand? What do I need to know? And where can I find the proof?

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Originally Posted by ymar

I have recently learned about the existence of Birkhoff's HSP theorem. A Google search gives me little insight into it. Could you please tell me where I could find any kind of deeper info? Is the proof very difficult to understand? What do I need to know? And where can I find the proof?

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I don't have much time, but there is an excellent discussion about this in Robinson. Report back if you have any more questions. Also, you may want to ask this at math.stackexchange.com there is a member there who specializes in group varieties.

I have taken a look at this, but need to put more thought into it. Every time I read something that involves proper classes I'm afraid that I'm being fooled.

However, he only writes about group varieties. Wikipedia doesn't distinguish this kind. Is it possible to find the proof of the general statement?