The core material is covered in *Lecture Notes by Stephen Simpson*, available online.

*Supplementary reading:*

A classic introduction to mathematical logic is *Mathematical Logic*, by Joseph Shoenfield, Association of Symbolic Logic, A K Peters/CRC Press, 2001.

If you would like to read more about quantifier elimination in algebraic structures, *Model Theory - An Introduction* by David Marker, Springer, 2002 is an excellent source (Chapter 3).

(An online version of the book is available for Penn State members (use a campus computer or the VPN server) at dx.doi.org/10.1007/b98860)

For set theory, *T. Jech, Set Theory* (dx.doi.org/10.1007/3-540-44761-X) is a comprehensive reference.