论文标题
跨性别的差分领域的模型完整性
Model completeness for the differential field of transseries with exponentiation
论文作者
论文摘要
令$ \ mathbb {t} $为对数指数跨性别的微分字段。我们表明，其自然指数函数将$ \ mathbb {t} $扩展是模型完整的，并且在本地O-Minimal。我们给出了相对于实际指数领域理论有效的这种扩展理论的公理化。我们调整了结果，以表明通过此指数函数及其自然限制的正弦和受限余弦功能的$ \ mathbb {t} $的扩展也是完整的模型，并且在本地O-nimimal。
Let $\mathbb{T}$ be the differential field of logarithmic-exponential transseries. We show that the expansion of $\mathbb{T}$ by its natural exponential function is model complete and locally o-minimal. We give an axiomatization of the theory of this expansion that is effective relative to the theory of the real exponential field. We adapt our results to show that the expansion of $\mathbb{T}$ by this exponential function and by its natural restricted sine and restricted cosine functions is also model complete and locally o-minimal.
