Solvability, Probability, Definability: the Collected Works of Emil L. Post: (Contemporary Mathematicians)

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.

Table of Contents:
Introduction, Martin Davies. [1] The generalized gamma functions. [51 Introduction to a general theory of elementary propositions. [14] Generalized differentiation. [17] Finite combinatory processes, Formulation I. [18] Polyadic groups. [19] The Two-Valued Iterative Systems of Mathematical Logic. [20] Absolutely unsolvable problems and relatively undecidable propositions account of an anticipation. [21] Formal reductions of the general combinatorial decision problem. [22] Recursively enumerable sets of positive integers and their decision problems. [23] A variant of a recursively unsolvable problem. [24] Note on a conjecture of Skolem. [26] Recursive unsolvability of a problem of Thue. [27] Conjuntos recurrentemente numerables de enteros positives y sus problemas de decision. [34] (with S. C. Kleene) The upper semi-lattice of degrees of recursive unsolvability. ABSTRACTS: [2] Discussion of problem 433. [3] Introduction to a general theory of elementary propositions. [4] Determination of all closed systems of truth tables. [6] On a simple class of deductive systems. [7] Visual intuition in Lobachevsky space. [8] Visual intuition in spherical and elliptic space: Einstein's finite universe. [9] A non-Weierstrassian method of analytic prolongation. [10] A new method for generalizing ex in the complex domain. [11] A simple geometric proof of the equality of the Brochardt angles of a triangle. [12] Theory of generalized differentiation. [13] The mth derivative of a function of a function; calculus of mth derivatives. [15] Polyadic groups (preliminary report). [16] Finite combinatory processes. Formulation. [25] Recursive unsolvability of a problem of Thue. [28] Degrees of recursive unsolvability (preliminary report). [291 [with Samuel Linial (who later changed his name to Samuel Gulden)] Recursive unsolvability of the deducibility, Tarski's completeness, and independence of axioms problems of propositional calculus. [30] Note on a relation recursion calculus. [31] Solvability, definability, provability; history of an error. [32] A necessary condition for definability for transfinite von Neumann-Godel set theory sets, with an application to the problem of the existence of a definable well-ordering of the continuum (preliminary report). [33] (with S. C. Kleene) The upper semi-lattice of degrees of recursive unsolvability. [List Permissions]