论文标题
伪计数模型
Pseudo-countable models
论文作者
论文摘要
每个数学结构都具有伪计数结构的基本扩展，即使它实际上可能是不可数量的，它在合适的集合理论的合适类模型中被认为是可计数的。通过布尔超能定理很容易证明了这一观察结果，可以使结果广泛地概括为无数模型的丰富领域。例如，Barwise扩展定理构成了伪计数模型 - ZF的每个伪计数模型都允许ZFC+V = L的模型结束扩展。实际上，伪算模型类别是一系列众多的理论世界，其中包含任何给定的设置理论模型的基本扩展，并在强迫扩展和解释模型的情况下封闭，同时又符合Barwise Extension定理，Keisler-Morley定理，重复定理，以及其他有限的序列序列，以及其他有限的序列。
Every mathematical structure has an elementary extension to a pseudo-countable structure, one that is seen as countable inside a suitable class model of set theory, even though it may actually be uncountable. This observation, proved easily with the Boolean ultrapower theorem, enables a sweeping generalization of results concerning countable models to a rich realm of uncountable models. The Barwise extension theorem, for example, holds amongst the pseudo-countable models -- every pseudo-countable model of ZF admits an end extension to a model of ZFC+V=L. Indeed, the class of pseudo-countable models is a rich multiverse of set-theoretic worlds, containing elementary extensions of any given model of set theory and closed under forcing extensions and interpreted models, while simultaneously fulfilling the Barwise extension theorem, the Keisler-Morley theorem, the resurrection theorem, and the universal finite sequence theorem, among others.
