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Computability in Combinatory Spaces
An Algebraic Generalization of Abstract First Order Computability
von Dimiter G. SkordevInhaltsverzeichnis
- 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.