Algorithmic Properties of Structures: Selected Papers of Erwin Engeler

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World Scientific, 1993 - Computers - 257 pages
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The work of Erwin Engeler in the logic and algebra of computer science has been influential but has become difficult to access because it has appeared in different types of publications. This collection of selected papers is therefore timely and useful. It represents 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 programs executed in a given class of mathematical structures, and is related to questions of correctness and provability of programs. This point of view allowed the generalization of classical Galois theory to the point of discussing the relation between structure and complexity of solution programs 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 with by expanding these structures into combinatory algebras.
 

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Contents

Logics of Algorithmic Properties
1
Syntax
31
Vol 72 Springer 1968 6476 31
49
Symp Auto
62
Symp Semantics
73
Mathem Logic in Com
87
Intern Symp on Theoretical Program
97
Galois Theory and the Structure of Problems
107
Math Found
131
Structural relations between programs and problems Int Congr
137
An Algebraization of Algorithmics
183
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