Monadic second order logic is the expansion of first order logic by quantifiers ranging over unary relations. We study the shared monadic second order theory of finite linear orders, i.e. the pseudofinite monadic second order theory of linear order, using a first order setup . We give explicit (and recursive) axioms and characterise the completions in terms of residue sequences. A connection with profinite algebra, in particular with the free profinite monoid on one generator, is established via extended Stone duality.

中文翻译：

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线性阶的伪有限二阶二阶理论

一元二阶逻辑是通过一元关系上的量词对一阶逻辑的扩展。我们使用一阶设置研究有限线性阶的共享单子二阶理论，即线性阶的伪有限单子二阶理论。我们给出了显式（和递归）公理，并根据残基序列描述了完成度。通过扩展的Stone对偶性，建立了与有限代数的连接，特别是与一个生成器上的自由有限monoid的连接。