论文标题
在$ \ Mathcal {C}^\ indcal $ reduced $ \ mathcal {c}^\ infty $ rings and应用程序的订单理论上
On the order theory for $\mathcal{C}^\infty$-reduced $\mathcal{C}^\infty$-Rings and applications
论文作者
论文摘要
在目前的工作中，我们对（$ \ MATHCAL {C}^{\ infty} - $ - 降低）$ \ MATHCAL {C}^{\ infty} - $ - $ - $ $ - $ - $ - $ - cite {rings1}（另请参见\ cite \ cite {bm2}）。特别是，我们应用了$ \ MATHCAL {C}^{\ infty} - $ - 字段（例如，每个这样的领域都是真正关闭）的顺序理论的一些结果，以对一般$ \ Mathcal {c}^{c}^{\ infty} - $ - $ - $ - 圆环的订单理论提出另一种方法。这表明对$ \ Mathcal {C}^{\ infty} - $ - 字段的类别的模型理论研究可能很有趣，并且对于开发“真实代数几何”的第一步也可能很有用，$ \ Mathcal {c}^{c}^{c}^{\ infty} - $ - $ - $ - $ - $ - $ - $ - $ - $ - ring。
In the present work we carry on the study of the order theory for ($\mathcal{C}^{\infty}-$-reduced) $\mathcal{C}^{\infty}-$-rings initiated in \cite{rings1} (see also \cite{BM2}). In particular, we apply some results of the order theory of $\mathcal{C}^{\infty}-$-fields (e.g., every such field is real closed) to present another approach to the order theory of general $\mathcal{C}^{\infty}-$-rings: "smooth real spectra" (see \cite{separation}). This suggests that a model-theoretic investigation of the class of $\mathcal{C}^{\infty}-$-fields could be interesting and also useful to provide the first steps towards the development of the "Real Algebraic Geometry" of $\mathcal{C}^{\infty}-$-rings.
