Pseudo-c-archimedean and pseudo-finite cyclically ordered groups

摘要

Robinson and Zakon gave necessary and sufficient conditions for an abelian ordered group to satisfy the same first-order sentences as an archimedean abelian ordered group (i.e., which embeds in the group of real numbers). The present paper generalizes theirwork to obtain similar results for infinite subgroups of the group of unimodular complex numbers. Furthermore, the groups which satisfy the same first-order sentences as ultraproducts of finite cyclic groups are characterized.