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Wilhelm Ackermann was a mathematical logician who worked with Hilbert in Göttingen.
Ackermann received his doctoral degree in 1925 with a thesis Begründung des "tertium non datur" mittels der Hilbertschen Theorie der Widerspruchsfreiheit written under Hilbert and was a proof of the consistency of arithmetic without induction. It was intended to be a consistency proof for elementary analysis although this proof contained significant errors.
Ackermann was also the main contributor to the development of the logical system known as the epsilon calculus, originally due to Hilbert. This formalism formed the basis of Bourbaki's logic and set theory.
From 1929 until 1948 he taught as a teacher at the Arnoldinum Gymnasium in Burgsteinfurt and in Luedenscheid. He was corresponding member of the Akademie der Wissenschaften in Göttingen, and was honorary professor at the Universität Münster.
In 1928, Ackermann observed that A(x, y, z), the z-fold iterated exponentiation of x with y, is an example of a recursive function which is not primitive recursive. A(x, y, z) was simplified to a function P(x, y) of 2 variables by Rozsa Peter whose initial condition was simplified by Raphael Robinson. It is the latter which occurs as Ackermann's function in today's textbooks. Also in 1928 the often reprinted book Grundzüge der Theoretischen Logik by Hilbert and Ackermann appeared.
Among Ackermann's later work are consistency proofs for set theory (1937), full arithmetic (1940) and type free logic (1952). Further there was a new axiomatization of set theory (1956), and a book Solvable cases of the decision problem (North Holland, 1954).
Article by: Walter Felscher, Tübingen
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