Some applications of Nevanlinna theory to mathematical logic: identities of exponential functions
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- by C. Ward Henson and Lee A. Rubel PDF
- Trans. Amer. Math. Soc. 282 (1984), 1-32 Request permission
Correction: Trans. Amer. Math. Soc. 294 (1986), 381.
Abstract:
In this paper we study identities between certain functions of many variables that are constructed by using the elementary functions of addition $x+y$, multiplication $x \cdot y$, and two-place exponentiation $x^y$. For a restricted class of such functions, we show that every true identity follows from the natural set of eleven axioms. The rates of growth of such functions, in the case of a single independent variable $x$, as $x \to \infty$, are also studied, and we give an algorithm for the Hardy relation of eventual domination, again for a restricted class of functions. Value distribution of analytic functions of one and of several complex variables, especially the Nevanlinna characteristic, plays a major role in our proofs.References
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Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 282 (1984), 1-32
- MSC: Primary 03B25; Secondary 03C05, 32A22
- DOI: https://doi.org/10.1090/S0002-9947-1984-0728700-X
- MathSciNet review: 728700