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err i think yes........
After Vai joined Zappa he started to mention Satrianis name around as he had taught him. Satch released a demo tape and then many musical publications got hold of it and it went from there.
No Django Reinhardt, Les Paul, Lowman Pauling, Steve Cropper, Reggie Young, Teenie Hodges, Larry Carlton?
Don't forget Charlie Christian, Wes Montgomery, Pat Metheney and John Mclaughlin
Yes, it is well documented that Vai took lessons when he was younger (pre-Zappa) from Joe; even Joe talks about it.
I went to a G3 concert a few years ago just to see Steve, even though Joe and Eric Johnson were there also. Kenny Wayne Shepherd opened for them, he was pretty good; I was, however, very unimpressed with Eric Johnson.
When Steve was done playing, I left. IMHO, Steve Vai is the most accomplished guitartist of his generation.
I personally think that Malmsteen is overated. I mean he is a great guitarist and you can not deny that, but he is so full of himself and there are plenty of people out there that are just as good but without the ego.
I listen to some classical, but I'm not really into it. Well, not the happy sounding ones. I've been trying to find some dark and ominous sounding classical/romantic period stuff, but I've had no luck.