Martin Löb

This article deals with the German mathematician Martin Löb, for the French actor with a similar name see Martin Loeb .

Martin Hugo Löb (born March 31, 1921 in Berlin ; † August 21, 2006 in Annen , Drenthe ) was a German mathematician . He worked in the field of mathematical logic and in 1955 published the Löb theorem named after him , which is based on an argument analogous to that in Curry's Paradox .

Life

Löb grew up in Berlin , but fled to Great Britain from the National Socialists shortly before the outbreak of World War II . There he was deported as an enemy alien in 1940 to an internment camp in Hay in Australia , where he was taught mathematics by inmates there at the age of 19. One of his teachers, Felix Behrend , later became a professor at Melbourne University .

In 1943 Löb was able to return to Great Britain and studied at the University of London after the war . There he became in 1951 the degree of PhD at Reuben Goodstein , who at that time at the University College in Leicester worked 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 worked for 20 years, becoming a reader and later professor of mathematical logic.

Löb was married and had two daughters. His wife Caroline was Dutch , and so he accepted a professorship at the University of Amsterdam in the early 1970s to succeed Beth .

plant

Löb worked in the field of mathematical logic , in particular he dealt with proof theory , modal logic and computability theory . In Leeds, he set up a Mathematical Logic Working Group, which became one of the leading centers in this field in Great Britain. In 1955 he formulated Löb's theorem and showed in it that so-called Henkin theorems, which claim that they can be proven, can be proven; he used Curry's paradox without naming his name , which is why it is sometimes referred to as Löb's paradox. The theorem is a reinforcement of Gödel's second incompleteness theorem : The latter says that in a sufficiently strong axiom system T the formalized statement "The system T is consistent " is unprovable if T is consistent. According to Löb's theorem, a contradiction could be deduced in T if the Henkin proposition "A contradiction follows from the consistency of T " could be derived in T (which is logically equivalent to "The system T is consistent"). So, based on Löb's theorem in T, the statement "The system T is consistent" cannot be derived.

Web links

• John J. O'Connor, Edmund F. Robertson :  Martin Löb. In: MacTutor History of Mathematics archive .
• Obituary , The Guardian , October 3, 2006
• Obituary , Institute for Logic, Language and Computation, University of Amsterdam

Individual evidence

1. ^ Löb, Martin Hugo: "Solution of a Problem of Leon Henkin", Journal of Symbolic Logic 20 (1955), 115-118, Paradoxon p. 117
2. ↑ Wolfgang Rautenberg : Introduction to Mathematical Logic . 3. Edition. Vieweg + Teubner , Wiesbaden 2008, ISBN 978-3-8348-0578-2 , pp. 218-219 .