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Dear Mrs Gordon,
Many thanks for your posting and for the compliment. I am delighted that your son is enjoying the material so far.
You ask ‘What else should I include to “count” him as having taken a high school level course in logic.” Well, all I can say is that, if he’s studied everything on your list, he’s well ahead of the game. However, I’m sending to you by email my schematic notes on mathematical logic which he may find of some use (as well as some other material). The notes are meant to be self-guiding but if he needs any help, please do get in touch.
Your son is lucky to have the opportunity to study at home. I was completely bored at school. I couldn’t wait to get out, and when that happy day arrived, I felt like a prisoner leaving gaol. I discovered logic at the age of 16 by reading E. J. Lemmon’s book (just then published) and I spent a summer when everyone else was at the beach determined not to let it get the better of me. My notes are based on Lemmon’s system, which I still consider one of the most elegant treatments of mathematical logic.
With every good wish,