Theory of Recursive Functions and Effective Computability

  title={Theory of Recursive Functions and Effective Computability},
  author={Jr. Hartley Rogers},
Central concerns of the book are related theories of recursively enumerable sets, of degree of un-solvability and turing degrees in particular. A second group of topics has to do with generalizations of recursion theory. The third topics group mentioned is subrecursive computability and subrecursive hierarchies 

Quasi-Degrees of Recursively Enumerable Sets

The basis of the modern theory of degrees of unsolvability is established in the article by Post [46] in which the notions of many-one (m-) reducibility, truth-table (tt-), bounded truth-table (btt-)

Turing Degrees of Isomorphism Types of Geometric Objects

Any Turing degree may occur as the least degree of an isomorphic copy of a structure of these kinds and it is shown that these structures may fail to have a least degree.

Arithmetical Hierarchy and Complexity of Computation

  • P. Hájek
  • Computer Science
    Theor. Comput. Sci.
  • 1979

Nondiamond Theorems for Polynomial Time Reducibility

  • R. Downey
  • Mathematics
    J. Comput. Syst. Sci.
  • 1992

On the Interplay Between Inductive Inference of Recursive Functions, Complexity Theory and Recursive Numberings

The present paper surveys some results from the inductive inference of recursive functions, which are related to the characterization of inferrible function classes in terms of complexity theory, and


Criteria are found for the transitivity and reflexivity of the reducibility relation defined by a class of ordered pairs of Boolean functions.

Bounds in the Turing Reducibility of Functions

A hierarchy of functions with respect to their role as bounds in the Turing reducibility of functions is introduced and studied. This hierarchy leads to a certain notion of incompressibility of sets

A Précis of Classical Computability Theory

This chapter introduces basic notions and results of Turing machines and readers already familiar with them can safely skip it.

Degrees of Total Algorithms versus Degrees of Honest Functions

A few theorems are proved elucidating the relationship between to different approaches to subrecursive degree theory and their roots in the theory of algorithms and Turing degrees.