论文标题
DP-FINITE FIELDS VI：DP-FINITE SHELAH猜想
Dp-finite fields VI: the dp-finite Shelah conjecture
论文作者
论文摘要
我们证明了Shelah猜想在NIP场上的DP-FINITE案例。如果K是DP-FINITE场，则K接收一个非平凡的可定义的Henselian评估环，除非K是有限的，真实的封闭或代数封闭的。结果，DP-FINITE场的猜想分类成立。此外，DP-FINITE值的田地是Henselian。最后，如果K是一个领域的不稳定的DP-FINITE扩展，那么K会承认独特的可定义V-Topology。
We prove the dp-finite case of the Shelah conjecture on NIP fields. If K is a dp-finite field, then K admits a non-trivial definable henselian valuation ring, unless K is finite, real closed, or algebraically closed. As a consequence, the conjectural classification of dp-finite fields holds. Additionally, dp-finite valued fields are henselian. Lastly, if K is an unstable dp-finite expansion of a field, then K admits a unique definable V-topology.
