published in 1936. In his Habilitationsschrift, finished in 1939, he determined the proof-theoretical strength of Peano arithmetic. This was done by a direct proof of the unprovability of the principle of transfinite induction, used in his 1936 proof of consistency, within Peano arithmetic. The principle can, however, be expressed in arithmetic, so that a direct proof of Gödel's incompleteness theorem followed. Gödel used a coding procedure to construct an unprovable formula of arithmetic. Gentzen's proof was published in 1943 and marked the beginning of ordinal proof theory. Publications (Lecture hold in Münster at the institute of Heinrich Scholz on 27 June 1936) Posthumous – Published by Paul Bernays. – Published by Paul Bernays. See also Bertrand Russell Notes References - (English translation). - an English translation. External links 1909 births 1945 deaths People from Greifswald University of Göttingen alumni Nazi Party members Academic staff of Charles University 20th-century German mathematicians German logicians People from the Province of Pomerania 20th-century German philosophers Deaths by starvation Nazis who died in prison custody German people who died in Soviet detention