论文标题
科恩般的一阶结构
Cohen-like first order structures
论文作者
论文摘要
我们研究与Fraïssé极限类似的不可数结构。 Fraïssé理论的标准归纳论证被强迫取代，因此我们获得的结构对集合理论的宇宙高度敏感。特别是，我们研究的通用结构仅存在于宇宙的通用扩展中。我们证明，在大多数有趣的情况下，无数的通用结构都是刚性的。此外，我们提供了一个（一致）的示例，以与整数作为其自动形态组的一组无数，密集的真实组合。
We study uncountable structures similar to the Fraïssé limits. The standard inductive arguments from the Fraïssé theory are replaced by forcing, so the structures we obtain are highly sensitive to the universe of set theory. In particular, the generic structures we investigate exist only in generic extensions of the universe. We prove that in most of the interesting cases the uncountable generic structures are rigid. Moreover, we provide a (consistent) example of an uncountable, dense set of reals with the group of integers as its automorphism group.
