1
vote
1answer
75 views

How to extract the sets “produced” by a axiomatic set theory, into some newly introduced collection?

Say I know well how to reason in a set theory, which for the sake of this question I'll call $\bf{ST}$, say one of those, it can by $\bf ZFC$. It's principally written down via first order logic and ...
5
votes
1answer
196 views

Foundational theories, their uses, interactions and comparisons?

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 ...
2
votes
1answer
88 views

Struggling with classes

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 ...
12
votes
3answers
458 views

Why is it worth spending time on type theory?

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 ...
2
votes
0answers
68 views

What are the main differences between set theory versus pure type systems?

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 ...
2
votes
2answers
168 views

Accessible formal specification and explanation of First Order Logic?

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 ...