Ha! Yeah, it seems that his name is pretty ubiquitous in mathematical logic, and he wrote or contributed to quite a number of publications. I had a professor for a sequence in mathematical logic who had Barwise as his thesis adviser. The professor obtained his doctoral degree from UW Madison when it still had Barwise, Kleene and Keisler so he would tell stories about some class he had with one or the other of them.

Barwise seems to have had quite a few interesting/powerful ideas. I've been wanting to read Vicious Circles for a while now, though I haven't gotten around to it.