当where子句包含LIST时使用LINQ

我有一个列表，我试图使用LINQ查询。T类型有一个属性是List 。我正试图查询我的列表 s List <属性只拉出那些List属性项与单独List中的项匹配的对象><用来过滤的U>。我的代码是这样的:

class T {
   List<U> Names;
}
class U {
}
//then I want to query a List of T by interrogating which T objects' Names property has the same items that I have a List < U > that I have created.
List<U> searchTermItems;
List<T> allObjects;
//Query allObjects and find out which objects' Name property items match the items in the searchTermItems list

var filtered = allObjects.Intersect(searchTermItems);

var filtered = allObjects.Where(x => x.Names.Intersect(searchTermItems).Any());