Example of an interpolation domain

Cahen et al. (J. Algebra 225 (2000) 794), have defined a domain to be an interpolation domain if, essentially, Lagrange interpolation can be done using integer-valued polynomials. They prove results indicating that in some cases every overring of an interpolation domain is again an interpolation domain, and they ask whether the statement holds in general. In the present note, we provide a counterexample to the general statement.