Amalgamation and Neat Embeddings in Algebraic Logic

It often happens that a theory designed originally as a tool for the study of a physical problem came subsequently to have purely mathematical interest. When such a phenomena occurs, the theory is usually generalized beyond the point needed for applications, the generalizations make contact with other theories (frequently in completely unexpected directions), and the subject becomes established as a new part of pure mathematics. The part of pure mathematics so created does not (and need not) pretend to solve the physical problem from which it arises; it must stand or fall on its own merits. Physics is not the only external source of mathematical theories; other disciplines (such as economics and biology) can play a similar role. A recent (and possibly somewhat surprising) addition to the collection of mathematical catalysts is formal logic; the branch of pure mathematics that it has precipitated will here be called algebraic logic. Since the dissertation belongs to the field of algebraic logic, our theorems will be formulated (and proved) for the algebraic counterpart of such logic, i.e., for certain classes of algebras.