Computability in Combinatory Spaces - Dimiter G. Skordev

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Résumé :
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....

Sommaire:
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.