AI 中文总结
研究大域相关性质，通过构建可定义集的树证明大玫瑰色域有界等，简化相关证明，明确不稳定性等，还揭示大玫瑰色域上序的性质。
AI 中文摘要
我们证明了大的玫瑰色域是有界的，并大幅简化了关于大的稳定域是可分闭的以及大的单域是有界的证明。我们的证明在一般拓扑设置下成立。通过构建可定义集的适当树，我们明确得到不稳定性、非单性和非玫瑰色性。我们还表明大玫瑰色域上的序具有伪实闭域上序的若干性质。
英文摘要
We show that large rosy fields are bounded, and substantially simplify the proofs that large stable fields are separably closed and that large simple fields are bounded. Our proofs go through in a general topological setting. We obtain instability, non-simplicity, and non-rosiness explicitly by building the appropriate trees of definable sets. We also show that orders on large rosy fields have several properties of orders on pseudo real closed fields.
Comments9 pages. Comments are welcome
