Martin Löb

Hugo Martin Loeb ( born March 31, 1921 in Berlin, † 21 August 2006 in Annen, Drenthe ) was a German mathematician. He worked in the field of mathematical logic and published in 1955 named after him sentence of Loeb, the analogous argument as in curries paradox is based.

Life

Loeb grew up in Berlin, but escaped shortly before the outbreak of World War II the Nazis to Britain. There he was deported as enemy alien in 1940 to an internment camp in Hay, Australia, where he was taught as a 19- year-old of local inmates in mathematics. One of his teachers, Felix Behrend, later became a professor at the University of Melbourne.

1943 Loeb could return to the UK after the war and studied at the University of London. There he obtained in 1951 the degree of PhD at Reuben Goodstein, who worked at that time at University College, Leicester, with the theme " A Methodological Characterization of Constructive Mathematics" and in the same year assistant professor (assistant lecturer ) at the University of Leeds. There he was for 20 years, was Reader and later Professor of Mathematical Logic.

Loeb was married and had two daughters. His wife Caroline was Dutch, so he took in the early 1970s as a professor at the University of Amsterdam as a successor to Beth.

Work

Loeb worked in the field of mathematical logic, in particular, he was concerned with proof theory, modal logic and computability theory. In Leeds he set up a working group Mathematical Logic, which became one of the leading centers in this field in the UK. He formulated the 1955 set of Leib and showed that so-called Henkin sentences that assert their own provability, are provable; while he used without attribution curries paradox, which is therefore sometimes referred to as Loeb's paradox. The theorem is a strengthening of Gödel's second incompleteness theorem: the latter states that in a sufficiently strong axiom system T is the formalized statement " The system T is consistent" is unprovable if T is consistent. After the set of Loeb now is that in T a contradiction could be derived if the Henkin sentence "From the consistency of T follows a contradiction " in T could be derived ( equivalent which logically "The system T is consistent "). So, due to the set of Loeb in T the statement " The system T is consistent " should not be inferred.