Discontinuities of provably correct operators on the provably recursive real numbers

Journal of Symbolic Logic 48 (4):913-920 (1983)
Abstract
In this paper we continue, from [2], the development of provably recursive analysis, that is, the study of real numbers defined by programs which can be proven to be correct in some fixed axiom system S. In particular we develop the provable analogue of an effective operator on the set C of recursive real numbers, namely, a provably correct operator on the set P of provably recursive real numbers. In Theorems 1 and 2 we exhibit a provably correct operator on P which is discontinuous at 0; we thus disprove the analogue of the Ceitin-Moschovakis theorem of recursive analysis, which states that every effective operator on C is (effectively) continuous. Our final theorems show, however, that no provably correct operator on P can be proven (in S) to be discontinuous
Keywords No keywords specified (fix it)
Categories (categorize this paper)
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
 
Download options
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 11,826
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA

No references found.

Citations of this work BETA

No citations found.

Similar books and articles
Analytics

Monthly downloads

Sorry, there are not enough data points to plot this chart.

Added to index

2009-01-28

Total downloads

1 ( #454,238 of 1,100,115 )

Recent downloads (6 months)

1 ( #304,144 of 1,100,115 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Start a new thread
Order:
There  are no threads in this forum
Nothing in this forum yet.