Aspects of N0-Categoricity

Abstract

Publisher Summary This chapter discusses the various aspects of N0-categoricity. The chapter describes classical algebraic theories of modules, rings, or groups. There are connections between N0-categoricity and the notions of model-completeness and QE (quantifier elimination). These connections can be exploited to deduce the question of the existence of N0-categorical structures of a given type to a fairly elementary calculation. N0-categorical modules in terms of their transitive constituents are also described in the chapter. There are many N0-categorical nilpotent groups of class 2. QE technology failed slightly, because most QE nilpotent groups are of exponent 4, which is not very satisfactory. It can be repaired by taking QE groups in a language with a predicate for the center. The chapter also describes the general model theory that includes stable No-categorical structures, and QE structures for small (microscopic) languages.