I'm looking to learn a little bit about polyadic and cylindric algebras, as part of an investigation into algebraic approaches to logic.
The only "text" that I can find for polyadic algebra is Halmos' and I've got to be honest, I don't like Halmos' writing style. (I've tried two different texts from him and the style doesn't work for me.)
For cylindric the only thing I can find there is the two volume series from Tarski, Henkin, and Monk. I can't seem to locate Part I in my library, and it seems hard to find to purchase.
I've found some limited papers which may suffice to give me an idea of what is going on, but I was wondering if anyone knew of any other papers/textbooks that had bits about these algebras?
Also as an additional question, I'm wondering whether it is worth my time to pursue polyadic/cylindric algebras. Have the category theory approaches to logic become more valuable than polyadic and/or cylindric approaches?
Thank you for any guidance you can provide.
Thanks for asking this, I'd wanted to ask almost the exact same question, word for word!
I don't have a very good answer, but I think the introductory book by Halmos and Givant 1988 ("Logic as algebra") is helpful. Is that one of the 2 books you mentioned? Knowing some algebraic geometry (such as the use of ideals) may help in understanding the book.
See also my question: simple exercise in Cylindric algebra
I'd like to discuss / share more ideas when I have time...