Fri Mar 24, 2017
60 Evans Hall, 4:10–5:10 PM
Françoise Point (FNRS-FRS (UMons))
On expansions of (ℤ, +, 0)
In the special case of the structure (ℤ, +, 0), we will consider the following model-theoretic question: given a well-behaved first-order structure, which kind of predicates can one add and retain model-theoretic properties of the structure one started with, such as stability- like properties, quantifier elimination in a reasonable language, decidability. We will review recent results on stability properties of expansions of (ℤ, +, 0) by a unary predicate and we will make the comparison with former results on the decidability and model-completeness of the corresponding expansions of (ℤ, +, 0, <) (and if time permits, with the corresponding expansions of the field of real numbers).