ACKERMANN, WILHELM. Solvable Cases of the Decision Problem. Amsterdam North-Holland 1954
8vo. Original printed stiff wrappers. Besides some very light wear to extremities, an excellent copy. VIII,114 pp.
First edition. Ackermann was a Ph.D. student of Hilbert at the University of Göttingen. Together they published the much important monograph 'Grunzüge der theoretischen Logik' (Principles of Theoretical Logic) in 1928. This book contained the first exposition ever of first-order logic and posed the problem of its completeness and the decision problem ('Entscheidungsproblem'). In 1929 Kurt Gödel established the completeness of first-order logic (this result is known as Gödel's completeness theorem). And in 1936 Alonzo Church and Allan Turing independently answered the decision problem in negative. However; in some cases the decision problem is solvable. Emil Post had shown in his dissertation 'Introduction to a general theory of elementary propositions' from 1921 that the weeker propositional logic is complete. The offered work by Ackermann is an important exposition of the cases in between were the decision problem is solvable.
DKK1000
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