Mathematical logic & its branches

[Cinitiator]

What branches of mathematical logic are there? I've taken formal logic (that is, the logic where one has various operators, like conjunction, disjunction, etc). What other fields of logic should I take to become better at mathematical logic? Which fields of logic are the most useful and essential?

 

[chiro]

Hey Cinitiator.

One idea to help includes looking at a computational logic implementation known as ProLog:

http://en.wikipedia.org/wiki/Prolog

This will give you a lot of experience if you use the platforms and get to used to the paradigm for these applications.

Getting used to using the software, doing a few queries and seeing how it all works and the feedback you will get will give you knowledge about how people think about not only describing logical systems, but also proving them or enumerating them.

 

[ThoralfSkolem]

There are four main branches of mathematical logic:

1. Set theory
2. Model theory
3. Computability and recursion theory
4. Proof theory

(At least this is how the Handbook of Mathematical Logic is divided.)

You can study a book which touches on all subjects. For example:

https://www.amazon.com/dp/1904987141/?tag=pfamazon01-20
https://www.amazon.com/dp/0387942580/?tag=pfamazon01-20

Or you can try an introductory book in a subject of your choice. If your major is maths then first learn set theory. If your major is computer science then first learn Computability theory.