A fun talk this afternoon in CMS from John Bell on “The Axiom of Choice in a Constructive Setting”, delivered with really engaging zest: went home with renewed enthusiasm to read the rest of Bell’s recent book which I started a few days ago (yes, yes, I should be concentrating on writing my book, but that’s another story).
If you don’t know it, The Axiom of Choice was published last year by College Publications (which is an admirable outfit, publishing some really good logic books at knock-down prices). The first four chapters are a zippy run-through the headline news about (1) The origins and status of AC, (2) maximal principles and Zorn’s Lemma, (3) math. applications of AC, and (4) consistency and independence of AC. But the largely-new-to-me stuff is in the chapters on (5) AC and intuitionist logic, (6) AC in category/topos/local set theories, (7) AC in constructive type theory. Unsurprisingly, given the author, this is admirably clear and full of stuff for philosophers to think about.
A must for the library!