Studying Boolean algebras with distinguished subalgebras, we establish the existence of continuum many simple superatomic Boolean algebras with distinguished subalgebra whose elementary theories are distinct and each of them lacks countably saturated models. The subalgebras coincide with the Boolean algebras modulo their Fréchet ideals.

中文翻译：

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具有可数饱和模型的可区分子代数的超原子布尔代数理论

研究具有特异子代数的布尔代数，我们建立了连续统的存在性，许多具有特异子代数的简单超原子布尔代数的基本理论是不同的，并且每个都缺乏可数饱和模型。子代数与以 Fréchet 理想为模的布尔代数一致。