On Rudimentarity, Primitive Recursivity and Representability

Reports on Mathematical Logic 55:73–85 (2020)
Download Edit this record How to cite View on PhilPapers
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.
No categories specified
(categorize this paper)
PhilPapers/Archive ID
Upload history
Archival date: 2021-02-21
View other versions
Added to PP index

Total views
8 ( #57,996 of 56,856 )

Recent downloads (6 months)
8 ( #51,327 of 56,856 )

How can I increase my downloads?

Downloads since first upload
This graph includes both downloads from PhilArchive and clicks on external links on PhilPapers.