Ackermann
# Wilhelm Ackermann

### Born: 29 March 1896 in Schoenebeck (Kr. Altena), Germany

Died: 24 Dec 1962 in Luedenscheid, Germany

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**Wilhelm Ackermann** was a mathematical logician who worked with Hilbert in Göttingen.

Ackermann received his doctoral degree in 1924 with a thesis written under Hilbert; its content was a consistency proof of arithmetic without induction. From 1927 until 1961 he taught as a teacher at the Gymnasien in Burgsteinfeld 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 Rosza Peter whose initial condition was simplified by Raphael Robinson (the husband of Julia Robinson); it is the latter which occurs as *Ackermann's function* in today's textbooks. Also in 1928 there appeared the often reprinted book *Grundzuege der Theoretischen Logik* by Hilbert and Ackermann.

Among Ackermann's later work there are consistency proofs for set theory (1937), full arithmetic (1940), 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, Tuebingen, 5 November 1996.*

**References (2 books/articles)**

JOC/EFR December 1996