Do you have any recommendations of what to study to understand category theory and more about the foundations of math? (Logic, type theory, computability & logic, model theory seem like contenders here)
You’re welcome! Foundation(s) of math is a huge and fascinating topic by itself, but if you’re more interested in the intricacy of abstraction hierarchies you should look no further than category theory, the Yoneda lemma, up up to doctrine theory. I love as a good introduction Category Theory by Awodey. As for the foundation of math, very good for dipping your toes are the first chapters of Marker’s introduction to model theory and the recently reprinted Set theory by Kunen (set theory models are a vast subject by themselves...)
Thanks for your enticing comment!
I understand your first point, but my math knowledge is not up to par to really understand point #2, and point #3 just makes me want to learn category theory. BTW, I also posted this question on the philosophy stackexchange: http://philosophy.stackexchange.com/questions/14689/how-does-abstraction-generalization-in-mathematics-fit-into-inductive-reasoning.
Do you have any recommendations of what to study to understand category theory and more about the foundations of math? (Logic, type theory, computability & logic, model theory seem like contenders here)
You’re welcome!
Foundation(s) of math is a huge and fascinating topic by itself, but if you’re more interested in the intricacy of abstraction hierarchies you should look no further than category theory, the Yoneda lemma, up up to doctrine theory. I love as a good introduction Category Theory by Awodey. As for the foundation of math, very good for dipping your toes are the first chapters of Marker’s introduction to model theory and the recently reprinted Set theory by Kunen (set theory models are a vast subject by themselves...)