论文标题
$ \ mathbb {r} _ {an，\ exp} $中的整数估价可定义的函数
Integer Valued Definable Functions in $\mathbb{R}_{an,\exp}$
论文作者
论文摘要
我们给出了Wilkie在$ \ mathbb {r} _ {an，\ exp} $中的一单元函数的结果，给出了两个变体，该函数在正整数上都采用整数值。只要功能比函数$ 2^x $增长，Wilkie表明该功能最终必须等于多项式。我们在更强的生长条件下显示了相同的结论，但仅假设该函数使值足够接近正整数的整数。在不同的变体中，我们表明，假设该函数在正整数的足够致密子集（例如素数）上（例如，在较强的生长界面）上比Wilkie的结果更强大。
We give two variations on a result of Wilkie's on unary functions defianble in $\mathbb{R}_{an,\exp}$ that take integer values at positive integers. Provided that the functions grows slower than the function $2^x$, Wilkie showed that is must be eventually equal to a polynomial. We show the same conclusion under a stronger growth condition but only assuming that the function takes values sufficiently close to a integers at positive integers. In a different variation we show that it suffices to assume that the function takes integer values on a sufficiently dense subset of the positive integers(for instance primes), again under a stronger growth bound than that in Wilkie's result.
