Recommendations for Intermediate Level Logics/Set Theory Books

I like Lorenz Halbeisen's "Combinatorial Set Theory" book. It also gives some basic introduction to logic, and how it is used in set theory. The book itself is very thorough and the parts I have read were mostly well-written.

Let me also add, that if you felt a bit shaky on the way logic was used in the set theory proofs, then perhaps it's best not to skip proofs that you already saw. Instead read them more thoroughly to find out new gems of understanding.

Logic textbook "less verbose" and quite general :

• Dirk van Dalen, Logic and Structure (5th ed - 2013).

As an alternative (with less topics covered) :

• Derek Goldrei, Propositional and Predicate Calculus : A Model of Argument (2005)

Set theory :

• Derek Goldrei, Classic set theory (1996).

You could have a go with H-D Ebbinghaus, J Flum: Finite Model Theory and T Jech: Set Theory.