Positive Complete Theories and Positive Strong Amalgamation Property

Abstract

We introduce the notion of positive strong amalgamation property and we investigate some universal forms and properties of this notion. Considering the close relationship between the amalgamation property and the notion of complete theories, we explore the fundamental properties of positively complete theories, and we illustrate the behaviour of this notion by bringing changes to the language of the theory through the groups theory.

Keywords

• h-inductive theory
• existentially closed
• complete theory
• positive amalgamation
• positive strong amalgamation
• mathematical model
• semantics