Algorithmic Properties of Structures

The work of Erwin Engeler in the logic and algebra of computer science has been influential in the development of the discipline but has become difficult to assess due to its having appeared in different types of publications. This collection of selected papers seeks to represent an original and coherent approach to the basic interrelationships between mathematics and computer science. The volume begins with the area of enrichment of classical model theory by languages which express properties representing the outcome of hypothetical computer programmes executed in a given class of mathematical structures, and is related to questions of correctness and provability of programmes. This point of view allowed the generalization of classical Galois theory to the point of discussing the relation between structure and complexity of solution programmes for problems posed in various mathematical theories. The algebraic approach is deepened and enlarged in the later papers by showing that the algorithmic aspects of any mathematical structure can be uniformly dealt wiht by expanding these structures into combinatory algebras.