Wilhelm Ackermann

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Wilhelm Ackermann (March 29, 1896, Herscheid municipality, Germany – December 24, 1962 Lüdenscheid, Germany ) was a German mathematician best known for the Ackermann function, an important example in the theory of computation.

Ackermann was awarded the Ph.D. by the University of Goettingen in 1925 for his thesis Begründung des "tertium non datur" mittels der Hilbertschen Theorie der Widerspruchsfreiheit, which was a consistency proof of arithmetic without induction. From 1929 until 1948, he taught at the Arnoldinum Gymnasium in Burgsteinfurt, and then at Lüdenscheid until 1961. He was also a corresponding member of the Akademie der Wissenschaften (Academy of Sciences) in Göttingen, and was an honorary professor at the Universität Münster (Westphalia).

In 1928, Ackermann helped David Hilbert turn his 1917-22 lectures on introductory mathematical logic into a text, Principles of Theoretical Logic. This text contained the first exposition ever of first order logic, and posed the problem of its completeness and decidability (Entscheidungsproblem). Ackermann went on to construct consistency proofs for set theory (1937), full arithmetic (1940), type-free logic (1952), and a new axiomatization of set theory (1956).

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Bibliography

1928. "On Hilbert's construction of the real numbers" in Jean van Heijenoort, ed., 1967. From Frege to Godel: A Source Book in Mathematical Logic, 1879-1931. Harvard Univ. Press: 493-507.
1950 (1928). (with David Hilbert) Principles of Theoretical Logic. Chelsea. Translation of 1938 German edition.
1954. Solvable cases of the decision problem. North Holland.

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