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I am very much interested in logic, study & interpretation of formal languages and proof theory and other aspects related to logic and semantics. But I believe I lack a good foundation. As part of degree, I only did one module on discrete mathematics which was not very deep.

I understand that logic is based lots of sets, relations and these aspects are important to understand other things that predicate and first order logic, semantic interpretation.....,

In short my question is, can I get some help about the books i can go through to master the important foundation of logic and then possibly books about important subtopics.

user203788
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Here's a very good, in depth walkthrough of the topics you might consider covering, in what order, and why

http://www.logicmatters.net/resources/pdfs/TeachYourselfLogic2016.pdf

Owain West
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  • It didn't even mention Inner Model Theory once, even though it contained a section on "ZFC, with all the bells and whistles..." :'( – Stefan Mesken Aug 04 '16 at 23:05