2015; Physical and Mathematical Sciences, 49 (1 (236): 52–60
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ON NON-CLASSICAL THEORY OF COMPUTABILITY

Nigiyan Nigiyan*

Received: 2025-02-12 · Published: 2015-03-16

© 2015 The Author(s) and the original publisher.

CC BY 4.0 This work is licensed under a Creative Commons Attribution 4.0 International License.
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Original title
ON NON-CLASSICAL THEORY OF COMPUTABILITY
Author
Nigiyan Nigiyan
Published
2015-03-16
Licence
Creative Commons Attribution 4.0 International

Abstract

Definition of arithmetical functions with indeterminate values of arguments is given. Notions of computability, strong computability and λ-definability for such functions are introduced. Monotonicity and computability of every λ-definable arithmetical function with indeterminate values of arguments is proved. It is proved that every computable, naturally extended arithmetical function with indeterminate values of arguments is λ-definable. It is also proved that there exist strong computable, monotonic arithmetical functions with indeterminate values of arguments, which are not λ-definable. The δ-redex problem for strong computable, monotonic arithmetical functions with indeterminate values of arguments is defined. It is proved that there exist strong computable, λ-definable arithmetical functions with indeterminate values of arguments, for which the δ-redex problem is unsolvable.
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