Wilhelm Ackermann

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Wilhelm Ackermann

Wilhelm Friedrich Ackermann (March 29, 1896, Herscheid

Herscheid

Herscheid is a municipality in the southern M?rkischer Kreis, in North Rhine-Westphalia, Germany....
municipality, Germany

Germany

Germany , officially the Federal Republic of Germany , is a country in Central Europe. It is bordered to the north by the North Sea, Denmark, and the Baltic Sea; to the east by Poland and the Czech Republic; to the south by Austria and Switzerland; and to the west by France, Luxembourg, Belgium, and the Netherlands....
– December 24, 1962 Lüdenscheid

Lüdenscheid

Germany

Mathematician

A mathematician is a person whose primary area of study and/or research is the field of mathematics....
best known for the Ackermann function

Ackermann function

In computability theory, the Ackermann function or Ackermann?P?ter function is a simple example of a computable function that is not Primitive recursive function....
, an important example in the theory of computation

Theory of computation

The theory of computation is the branch of computer science that deals with whether and how efficiently problems can be solved on a model of computation, using an algorithm....
.

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 apparently without full Peano induction (although it did use e.g.

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Encyclopedia

Wilhelm Friedrich Ackermann (March 29, 1896, Herscheid

Herscheid

Herscheid is a municipality in the southern M?rkischer Kreis, in North Rhine-Westphalia, Germany....
municipality, Germany

Germany

Lüdenscheid

Germany

Mathematician

A mathematician is a person whose primary area of study and/or research is the field of mathematics....
best known for the Ackermann function

Ackermann function

Theory of computation

Steinfurt

Steinfurt is a town in North Rhine-Westphalia, Germany. It is the capital of the district of Steinfurt ....
, and then at Lüdenscheid

Lüdenscheid

L?denscheid is a town in the M?rkischer Kreis district, in North Rhine-Westphalia, Germany. It is located in the Sauerland region. L?denscheid is seat of the administration of the M?rkischer Kreis district....
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

Westphalia

Westphalia is a region in Germany, centred on the cities of Bielefeld, Bochum, Dortmund, Gelsenkirchen, M?nster, and Osnabr?ck and included in the states of North Rhine-Westphalia and Lower Saxony....
).

In 1928, Ackermann helped David Hilbert

David Hilbert

David Hilbert was a Germany mathematician, recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries....
turn his 1917-22 lectures on introductory mathematical logic

Mathematical logic

Mathematical logic is a subfield of mathematics and logic with close connections to computer science and philosophical logic. The field includes the mathematical study of logic and the applications of formal logic to other areas of mathematics....
into a text, Principles of Theoretical Logic
Principles of Theoretical Logic

Principles of Mathematical Logic is the 1950 American translation of the 1938 second edition of David Hilbert's and Wilhelm Ackermann's classic text Grundz?ge der theoretischen Logik, on elementary mathematical logic....
. This text contained the first exposition ever of first-order logic

First-order logic

First-order logic is a formal deductive system used in mathematics, philosophy, linguistics, and computer science. It goes by many names, including: first-order predicate calculus , the lower predicate calculus, the language of first-order logic or predicate logic....
, and posed the problem of its completeness

Gödel's completeness theorem

G?del's completeness theorem is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic Provability logic in first-order logic....
and decidability (Entscheidungsproblem

Entscheidungsproblem

In mathematics, the Entscheidungsproblem is a challenge posed by David Hilbert in 1928. The Entscheidungsproblem asks for an algorithm that will take as input a description of a formal language and a mathematical statement in the language and produce as output either "True" or "False" according to whether the statement is true or false....
). Ackermann went on to construct consistency proof

Consistency proof

In logic, a consistent theory is one that does not contain a contradiction. The lack of contradiction can be defined in either semantic or syntactic terms....
s for set theory

Set theory

Set theory is the branch of mathematics that studies Set , which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics....
(1937), full arithmetic (1940), type-free logic (1952), and a new axiomatization of set theory (1956).

Bibliography

1928. "On Hilbert's construction of the real number
Real number

In mathematics, the real numbers may be described informally in several different ways. The real numbers include both rational numbers, such as 42 and −23/129, and irrational numbers, such as pi and the square root of two; or, a real number can be given by an infinite decimal representation, such as 2.4871773339...., where the digits co...
s" in Jean van Heijenoort
Jean Van Heijenoort

Jean Louis Maxime Van Heijenoort was a pioneer historian of mathematical logic. He was also a personal secretary to Leon Trotsky from 1932 to 1939, and from then until 1947, an American Trotskyist activist....
, ed., 1967. From Frege to Godel: A Source Book in Mathematical Logic, 1879-1931. Harvard Univ. Press: 493-507.
1950 (1928). (with David Hilbert
David Hilbert

David Hilbert was a Germany mathematician, recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries....
) Principles of Theoretical Logic
Principles of Theoretical Logic

Principles of Mathematical Logic is the 1950 American translation of the 1938 second edition of David Hilbert's and Wilhelm Ackermann's classic text Grundz?ge der theoretischen Logik, on elementary mathematical logic....
. Chelsea. Translation of 1938 German edition.
1954. Solvable cases of the decision problem
Decision problem

In computability theory and computational complexity theory, a decision problem is a question in some formal system with a yes-or-no answer, depending on the values of some input parameters....
. North Holland.

External links

at Stetson University
Stetson University

Stetson University is an independent, private, co-educational, liberal arts university in Florida, USA. In the 2008 U.S. News and World Report guide to America's Best Colleges, Stetson ranks second in the category of Southern Masters-granting institutions....