Books on logic can be found in the Mathematics Library Stacks currently located at Main Library 1 East shelved under call number 511.3 to 511.4 during the renovation of Altgeld Hall.
The discipline of Mathematical Logic is a rather historical umbrella encompassing the fields of Model Theory, Set Theory, Descriptive Set Theory, Computability Theory (also known as Recursion Theory), Proof Theory, and Universal Algebra.
Model Theory
Descriptive Set Theory
Set Theory