I am a student who is working Lie Theory. I want to start read theory of logics. I just need some reference and I have few questions regarding this,
i) will studying theory of logics will improve my theorem proving ability in 'other branch' of mathematics?
ii) is there any results in mathematics, (I am sure there are) (say in algebra particularly in group theory) proof of which is made easy through the approaches and techniques in theory of logics?
iii) where to start reading logic theory and which are good text books in logic theory for the beginners.
I have read Paul R.Halmos 's Naive Set Theory book completely. But I haven't done all the exercises. This is the amount of knowledge I have regarding theory of logics.
I hope I am not confusing between theory of sets and theory of logics.
Thanks for your valuable suggestions.