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Index sets for computable differential equations
Mathematical Logic Quarterly 50 (4-5):329-344 (2004)
Abstract
Index sets are used to measure the complexity of properties associated with the differentiability of real functions and the existence of solutions to certain classic differential equations. The new notion of a locally computable real function is introduced and provides several examples of Σ04 complete setsOther Versions
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References found in this work
Which set existence axioms are needed to prove the cauchy/peano theorem for ordinary differential equations?Stephen G. Simpson - 1984 - Journal of Symbolic Logic 49 (3):783-802.
Index sets for Π01 classes.Douglas Cenzer & Jeffrey Remmel - 1998 - Annals of Pure and Applied Logic 93 (1-3):3-61.
A computable ordinary differential equation which possesses no computable solution.Marian Boylan Pour-el - 1979 - Annals of Mathematical Logic 17 (1):61.
The wave equation with computable initial data whose unique solution is nowhere computable.Marian B. Pour-El & Ning Zhong - 1997 - Mathematical Logic Quarterly 43 (4):499-509.
Index sets for ω‐languages.Douglas Czenzer & Jeffrey B. Remmel - 2003 - Mathematical Logic Quarterly 49 (1):22-33.
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