This paper concerns Banach algebras which are real or * algebras and possess a unit. The principal method of attack is via an ordering of the algebra, the positive cone being the closure of the set of sums of squares (sums of elements xx*) in contrast to the positive open cone used by Raikov [9](3) and others. An important role is played by an identity on… (More)

Tarski is famous for his widely accepted conceptual analysis (or, in his terms, “explication”) of the notion of truth for formal languages and the allied notions of satisfaction, definability, and logical consequence. From an historical point of view, two questions are of interest. First, what motivated Tarski to make these analyses, and second, what led to… (More)

The semantical concepts, such as satisfaction, truth, and model, form the subject matter of a field known as the theory of models. I am going to discuss today several related recent developments in this field. They all lie in one particular area which is indicated by the title and which will be described more fully in a moment. However, some introductory… (More)