Shelah、Stupp和Muchnik迭代与一元二阶逻辑片断的相容性
Compatibility of Shelah and Stupp's and Muchnik's iteration with fragments of monadic second order logic
摘要：
我们研究了Shelah-Stupp和Muchnik意义上的迭代理论之间的关系，以及几种逻辑的基结构理论。这些逻辑是从一元二阶逻辑中的集合量化对某些子集的限制中获得的，例如，有限集、链和链的有限并。我们表明，这些理论的Shelah-Stupp迭代可以减少到相应的理论的基础结构。这对于Muchnik的迭代是失败的。
英文摘要：
We investigate the relation between the theory of the iterations in the sense of Shelah-Stupp and of Muchnik, resp., and the theory of the base structure for several logics. These logics are obtained from the restriction of set quantification in monadic second order logic to certain subsets like, e.g., finite sets, chains, and finite unions of chains. We show that these theories of the Shelah-Stupp iteration can be reduced to corresponding theories of the base structure. This fails for Muchnik's iteration.
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。
