Problems on the Generation of Finite Models

Recently, the subject of model generation has received much attention. By model generation we mean the automated generation of finite models of a given set of logical formulas. In this note, we present some problems on the generation of finite models. The purpose is two-fold: (1) to offer some test problems for model generation programs; and (2) to show the potential applications of such programs. Some of the problems are easy, some are hard and even open. We also give a new result in combinatory logic, which says that the fragment {B, N 1 } does not possess the strong fixed point property.