Computability in Combinatory Spaces von Dimiter G. Skordev | An Algebraic Generalization of Abstract First Order Computability | ISBN 9789401051651

Computability in Combinatory Spaces

An Algebraic Generalization of Abstract First Order Computability

von Dimiter G. Skordev
Buchcover Computability in Combinatory Spaces | Dimiter G. Skordev | EAN 9789401051651 | ISBN 94-010-5165-8 | ISBN 978-94-010-5165-1

Computability in Combinatory Spaces

An Algebraic Generalization of Abstract First Order Computability

von Dimiter G. Skordev

Inhaltsverzeichnis

  • I. Computational Structures and Computability on them.
  • 1. Computational structures.
  • 2. Computability of partial functions with respect to a given computational structure.
  • 3. On a procedure for generating the unary partial recursive functions.
  • 4. On the interconnection between programmability in a FP - system and ?- computability.
  • 5. Computability of multiple-valued functions with respect to a given computational structure.
  • 6. The recursively enumerable binary relations considered as multiple-valued functions.
  • 7. On the notions of prime and search computability.
  • 8. Computability in the case of unproductive termination taken into account.
  • II. Combinatory Spaces.
  • 1. The notion of combinatory space.
  • 2. The companion operative space of a combinatory space.
  • 3. Iteration in combinatory spaces.
  • 4. On least fixed points in partially ordered sets.
  • 5. The companion operative space of an iterative combinatory space.
  • 6. Left-homogeneous mappings and least fixed points connected with them.
  • 7. Some formal systems for the theory of iterative combinatory spaces.
  • III. Computability in Iterative Combinatory Spaces.
  • 1. Explicit and fixed-point definability in partially ordered algebras.
  • 2. Computable elements and mappings in iterative combinatory spaces.
  • 3. Representation of the partial recursive functions in iterative combinatory spaces.
  • 4. The First Recursion Theorem for iterative combinatory spaces.
  • 5. Application of the First Recursion Theorem to some concrete iterative combinatory space.
  • 6. Normal Form Theorems for computable elements and mappings in iterative combinatory spaces.
  • 7. Universal computable elements in iterative combinatory spaces.
  • 8. A notion of search computability in iterative combinatory spaces.
  • 9. On the formalization of the proof of theFirst Recursion Theorem.
  • References.
  • Additional Bibliography.
  • Index of Names.
  • Index of Definitions.