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Some applications of Nevanlinna theory to mathematical logic: identities of exponential functions

1984; American Mathematical Society; Volume: 282; Issue: 1 Linguagem: Inglês

10.1090/s0002-9947-1984-0728700-x

1088-6850

C. Ward Henson, Lee A. Rubel,

Meromorphic and Entire Functions

In this paper we study identities between certain functions of many variables that are constructed by using the elementary functions of addition x + y x+y , multiplication x ⋅ y x \cdot y , and two-place exponentiation x y 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 x , as x → ∞ 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.