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Some undecidable problems involving elementary functions of a real variable

  • Daniel Richardson

Extract

Let E be a set of expressions representing real, single valued, partially defined functions of one real variable. E* will be the set of functions represented by expressions in E.

If A is an expression in E, A(x) is the function denoted by A.

It is assumed that E* contains the identity function and the rational numbers as constant functions and that E* is closed under addition, subtraction, multiplication and composition.

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References

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[1]Davis, M., Putnam, H., and Robinson, J., The decision problem for exponential Diophantine equations, Annals of Mathematics, vol. 74 (1961), pp. 425436.

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