Question: I want to have an XML attribute without any value, which simply has one meaning when it exists or does not exist.

Is that valid?

Answer: 
No.

Boolean attributes in XML are of the form `foo="foo"`.

Even in SGML, you must provide the value, (it is the name, `=` and quotes that you can omit, which is why you have things like `<select multiple>` in HTML).
You can have an attribute whose only permitted value is the empty string, "". I'm not sure it's good design, though; I would normally suggest a boolean attribute with values true/false, and a default value of false.