稠密linear order的闭区间有限并格的模型完全性性
Model-completeness for the lattice of finite unions of closed intervals of a dense linear order
摘要：
设I是一个稠密的线性序，有左端点但没有右端点。我们考虑I的闭区间的有限并格L（I）.这个格在o-极小性的设置中自然出现，因为这些恰好是I的任何o-极小展开中的闭可定义集。我们的主要结果表明，L（I），由空集和I的最小元素（视为单元素子集）以及四个一元函数的常数展开的格，是模型完备的。主要结果的证明利用了作者博士论文中关于弱一元二阶理论的已有结果。
英文摘要：
Let I be a dense linear order with a left endpoint but no right endpoint. We consider the lattice L(I) of finite unions of closed intervals of I. This lattice arises naturally in the setting of o-minimality, as these are precisely the closed definable sets in any o-minimal expansion of I. Our main result says that L(I), the expansion of the lattice by constants for the empty set and the smallest element of I (viewed as a singleton subset) as well as four unary functions, is model-complete. The proof of the main result makes use of previous results regarding the weak monadic second order theory of I from the authors PhD thesis.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
