Nondefinability results for expansions of the field of real numbers by the exponential function and by the restricted sine function
Nondefinability results for expansions of the field of real numbers by the exponential function and by the restricted sine function
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通过指数函数和受限正弦函数展开实数域的不可定义性结果
DOI：
10.2307/2275634
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发表时间：
1997
影响因子：
0.6
通讯作者：
R. Bianconi
中科院分区：
文献类型：
--
作者：
R. Bianconi
本文证明了正弦函数不受任何限制，（开的和非空的）区间是可定义的，在R，+，·，×，<，exp，常数ε中，并且没有指数函数的限制，（开的非空的）区间可定义在[R，+，·，<，sin 0，常数n]中，其中sin 0（x）= sin（x），x ∈ [-π，π]，且sin 0（x）= 0，x ∈ [-π，π].
Abstract We prove that no restriction of the sine function to any (open and nonempty) interval is definable in 〈R, +, ·, ×, <, exp, constants〉, and that no restriction of the exponential function to an (open and nonempty) interval is definable in 〈R, +, ·, <, sin0, constants〉, where sin0(x) = sin(x) for x ∈ [—π, π], and sin0(x) = 0 for all x ∉ [—π, π].