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- Title
ON RUDIMENTARITY, PRIMITIVE RECURSIVITY AND REPRESENTABILITY.
- Authors
SALEHI, Saeed
- Abstract
It is quite well-known from Kurt G¨odel's (1931) ground-breaking Incompleteness Theorem that rudimentary relations (i.e., those definable by bounded formulae) are primitive recursive, and that primitive recursive functions are representable in sufficiently strong arithmetical theories. It is also known, though perhaps not as well-known as the former one, that some primitive recursive relations are not rudimentary. We present a simple and elementary proof of this fact in the first part of the paper. In the second part, we review some possible notions of representability of functions studied in the literature, and give a new proof of the equivalence of the weak representability with the (strong) representability of functions in sufficiently strong arithmetical theories.
- Subjects
INCOMPLETENESS theorems; RECURSIVE functions; EVIDENCE
- Publication
Reports on Mathematical Logic, 2020, Issue 55, p73
- ISSN
0137-2904
- Publication type
Article
- DOI
10.4467/20842589RM.20.004.12436