Post is best known for his work on polyadic groups, RecursivelyEnumerable sets, and degrees of unsolvability, as well as for his contribution to the unsolvability of problems in combinatorial mathematics. He introduced the concepts of completeness and consistency in a paper on truth-table methods which developed from the work of his doctoral thesis. He attributed these methods to his teacher at Columbia, C J Keyser, rather than to Charles Peirce and E Schröder as had been done previously. In the 1920's Post proved results similar to those which Gödel, Church and Turing discovered later, but he did not publish them. He reason he did not publish was because he felt that a 'complete analysis' was necessary to gain acceptance.
In 1936 he proposed what is now known as a Post machine, a kind of automaton which predates the notion of a program which von Neumann studied in 1946.
From: http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Post.html