Solvability, Provability, Definability: The Collected Works of Emil L.Post - Contemporary Mathematicians (Hardback)

Emil Post was a pioneer of twentieth century mathematical logic whose influence on what has come to be caned computer science is particularly remarkable considering his lack of any contact with computing machines. Although his initial contributions were to mathematical analysis, Post was caught up in the excitement generated by the pubhcation of Principia Mathematica purporting to demonstrate that all of mathematics could and should be regarded as a branch of logic. Post's approach, revolutionary for the second decade of the century, was to study logical systems like those in Principia, from the outside, using ordinary mathematical methods. His investigations led him not only to set forth what has become the standard paradigm for studying logical systems, but also to pursue two important generalizations: Post extended the two truth values of classical logic to an arbitrary number. Moreover, by showing how a system of logic could be viewed as a kind of general combinatorial system, Post provided the basis for much of modern computer science and was led to anticipate the later findings of Gbdel, Church, and Turing regarding undecidability. Post's later work included the first example of the unsolvabifity of a mathematical problem that had not originally arisen in the field of logic as well as the founding of the modern theory of recursively enumerable sets and of the theory of degrees of unsolvability. His work and point of view had an immense impact on a generation of young researchers. In this edition of Post's collected works, Martin Davis pays tribute to the profound influence of an original thinker, an inspiring and demanding teacher who overcame severe disabilities in continued devotion to his science and his students.