# Emil Leon Post

Emil Leon Post ( born February 11, 1897 in Augustow, Poland, † April 21, 1954 in New York, USA ) was a Polish- American mathematician and logician.

## Life and work

Post was a Polish- Jewish family that emigrated from the then part of Poland belonging to Russia in 1904 in the United States when he was still a child. He studied at the City College of New York ( completion 1917) and at Columbia University until his PhD, which he completed at Cassius Keyser 1920. Even before receiving his first diploma, he wrote an original work on differential operators with non- integer degrees, which was not published until 1930. In his dissertation, Introduction to a general theory of elementary propositions, he proved the completeness and consistency of the propositional logic calculus of Principia Mathematica by introducing truth tables. This he was able to generalize well for many-valued logics. He also established in consideration of the logic, as a method for generating words having a finite number of inference rules in a finite alphabet. After achieving the doctoral degree at Princeton, he came back in 1921 the discovery of later proven by Kurt Gödel 's incompleteness very close. But he did not publish anything, because it its own work on this subject is not released yet mature enough. In 1924 he moved to Columbia University. From 1927 he was a high school teacher of mathematics. In 1932 he went to the City College of New York and was thus again high school teacher. However, he had to because of a mental illness to give up his job and returned only in 1936 back to the university.

In the same year, he developed a machine model in computability theory, which is just as powerful as the Turing machine simultaneously developed. In 1947 he showed that the word problem recursively unsolvable in semigroups is (post- cal correspondence problem ). He is a co-founder of the theory of recursive functions.

Post suffered like Kurt Gödel from manic -depressive attacks, which first appeared during the time in Princeton. He was therefore several times in mental hospitals, where he, as was usual at that time, treated with electroconvulsive therapy. Shortly after such a treatment, he died of heart attack.

He was married in 1929 and had a child.

Among his pupils was Martin Davis.

## Work to polyvalent propositional logic

Emil Leon Post has already considered in his thesis and then regardless of Łukasiewicz and about the same time systems polyvalent propositional logic. Post developed these systems in the context of the study of classical propositional logic, in particular its functional completeness. Post Office launches an arbitrary finitely systems and discussed the case that besides the value 1 other quasi truth values can still be excellent. He used it as a negation the so-called post - negation and as an alternative the Łukasiewicz - Tarski alternative. It can be found at Post an implication which is a coupling of the Łukasiewicz - Tarski implication and the Gödel implication and post- implication is called.