On Rudimentarity, Primitive Recursivity and Representability
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RIS BIB ENDNOTEOn Rudimentarity, Primitive Recursivity and Representability
Publication date: 20.08.2020
Reports on Mathematical Logic, 2020, Number 55, pp. 73-85
https://doi.org/10.4467/20842589RM.20.004.12436Authors
On Rudimentarity, Primitive Recursivity and Representability
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.
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Information: Reports on Mathematical Logic, 2020, Number 55, pp. 73-85
Article type: Original article
Research Institute for Fundamental Sciences University of Tabriz, 29 Bahman Boulevard P.O.Box 51666-16471, Tabriz, Iran
Published at: 20.08.2020
Received at: 01.11.2019
Article status: Open
Licence: CC BY-NC-ND
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