The fundamental ideas concerning computation and recursion naturally find their place at the interface between logic and theoretical computer science. The contr

Once we have accepted a precise replacement of the concept of algo rithm, it becomes possible to attempt the problem whether there exist well-defined collection

Classic graduate-level introduction to theory of computability. Discusses general theory of computability, computable functions, operations on computable functi

..."The book, written by one of the main researchers on the field, gives a complete account of the theory of r.e. degrees. .... The definitions, results and pro

First English translation of revolutionary paper (1931) that established that even in elementary parts of arithmetic, there are propositions which cannot be pro