… of computability by introducing a rigorously defined notion of a Turing-computable function. It
… definition that Turing-computable functions are effectively computable. The hypothesis that, …

… what logic it induces. The goal of this paper is to introduce a basic logic of computability
and … Computability is a property of computational problems, or problems for short, sometimes …

The theme of this book is formed by a pair of concepts: the concept of formal language as
carrier of the precise expression of meaning, facts and problems, and the concept of algorithm …

… In this course we will learn two basic systems of logic—propositional logic and predicate
logic. Before that we use (even simpler) equational logic as the first example and get the feeling …

… II, Computable Functions, and Part III, Logic and Arithmetic, will suffice. In Part II we describe
the notion of computability, … propositional logic and give an overview of predicate logic and …

… classification of computable number-theoretic functions according to the logical complexity
of … Assuming R is computable, we can decide which by a case analysis. This comment also …

… of computability and … computability theory and logic, as well as to students of computer
science and mathematics who are interested in the history of and philosophy behind computability …

… text, or supplementary text, in courses in mathematical logic or in the theory of computability.
… of division by 2 gives rise to a singulary function which we write x/2. The domain of x/2 is the …

… and (ii) the degrees of the relation in computable models. The current best result for two-element
degree spectra for computable models is provided by the following result of Hirschfeldt. …

… first-order logic than any other proposed logic of … logic, and how might one axiomatize
dynamic logic? We give bounds on the validity problem for some special cases, including a Π 0 2 -…