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Title:
On Transitive Closures of Two-dimensional Strongly Positive Arithmetical Sets
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Elementary mathematics; Arithmetic ; Mathematics ; Algorithm
Uncontrolled Keywords:
Positive ; Strongly positive ; Arithmetical set ; Dimension ; Signature. 1. Introduction
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Abstract:
The notions of positive and strongly positive arithmetical set are considered in ([1]-[3] ). It is noted in [3] that the transitive closure of any 2-dimensional strongly positive set is primitive recursive. In this article a more strong statement is proved: the transitive closure of any 2-dimensional strongly positive set is defined by an arithmetical formula in the signature (0,=, < ,S), where S(x)=x+1.