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)
DOI 10.2307/2274131
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 43,728
Through your library

References found in this work BETA

Countable Algebra and Set Existence Axioms.H. M. Friedman - 1983 - Annals of Pure and Applied Logic 25 (2):141.

Add more references

Citations of this work BETA

Hilbert's Program Revisited.Panu Raatikainen - 2003 - Synthese 137 (1):157-177.
Countable Algebra and Set Existence Axioms.H. M. Friedman - 1983 - Annals of Pure and Applied Logic 25 (2):141.
Measure Theory and Weak König's Lemma.Xiaokang Yu & Stephen G. Simpson - 1990 - Archive for Mathematical Logic 30 (3):171-180.
Factorization of Polynomials and °1 Induction.S. G. Simpson - 1986 - Annals of Pure and Applied Logic 31 (2):289.

View all 27 citations / Add more citations

Similar books and articles

Analytics

Added to PP index
2009-01-28

Total views
26 ( #331,293 of 2,264,683 )

Recent downloads (6 months)
1 ( #863,502 of 2,264,683 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature