Which set existence axioms are needed to prove the cauchy/peano theorem for ordinary differential equations?

Journal of Symbolic Logic 49 (3):783-802 (1984)
Abstract
We investigate the provability or nonprovability of certain ordinary mathematical theorems within certain weak subsystems of second order arithmetic. Specifically, we consider the Cauchy/Peano existence theorem for solutions of ordinary differential equations, in the context of the formal system RCA 0 whose principal axioms are ▵ 0 1 comprehension and Σ 0 1 induction. Our main result is that, over RCA 0 , the Cauchy/Peano Theorem is provably equivalent to weak Konig's lemma, i.e. the statement that every infinite {0, 1}-tree has a path. We also show that, over RCA 0 , the Ascoli lemma is provably equivalent to arithmetical comprehension, as is Osgood's theorem on the existence of maximum solutions. At the end of the paper we digress to relate our results to degrees of unsolvability and to computable analysis
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: 11,392
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
Peter Clark (1990). Explanation in Physics: Explanation in Physical Theory. Royal Institute of Philosophy Supplement 27:155-175.

View all 7 citations

Similar books and articles
Analytics

Monthly downloads

Added to index

2009-01-28

Total downloads

4 ( #259,000 of 1,102,934 )

Recent downloads (6 months)

2 ( #183,209 of 1,102,934 )

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.