Practice Problems on the Elimination of Quantifiers

Question

In a recent answer, JDH gave a remarkable proof that the integers are not definable in the structure $(\mathbb{Q},+,<)$ using Quantifier Elimination. Since I already have the old Enderton book, are there other texts that provide problems that can give the reader some practice using Quantifier Elimination? Thanks!

Answer 1

Model theory texts typically have a section devoted to quantifier elimination.

For example, David Marker's book (google books link) shows quantifier elimination for the theories of dense linear orders, divisible abelian groups, presburger arithmetic, algebraically closed fields, and real closed fields all in the section pointed to there. The exercises for that particular chapter have some simple theories to work out quantifier elimination for yourself as well.

Other parts of the book have scattered results on some other theories, and some general theorems that can help with proving quantifier elimination.