Until now, I heard that there are some theories for building mathematical objects (or at least it is what it seems to my poor knowledge). Some of these are: Set theory; Logic; Category theory; Type ...
I am still struggling with the concept of classes in ZF set theory. From Jech, Set Theory, p.5: That means: For every formula $\varphi(x)$ there is a class (which is definable). There are ...
Looking around there are three candidates for "foundations of mathematics": set theory category theory type theory There is a seminal paper relating these three topics: From Sets to Types to ...
According to wikipedia, a pure type system: ...is a form of typed lambda calculus that allows an arbitrary number of sorts and dependencies between any of these... Pure type systems may ...
I am trying to get good at proofs by working through How To Prove It. Unfortunately I am very bothered by the fact that I do not understand all the formalities in First Order Logic + set theory ...