I have sometimes heard speakers at seminars refer to named theorems or definitions by prefacing them with the phrase "so-called". For example,
- "the so-called Theorem of Highest Weight. . ."
- "the so-called Hilbert Theorem 90. . ."
- "the so-called Galois group of an extension. . ."
Some of my teachers at my institute also use this phrase in the above manner quite regularly. This is not done repeatedly with the same object, of course. I think that the speaker uses the phrase "so-called" to emphasize that a theorem is being named, or that a definition is being made. I have certainly never seen the phrase being used in textbooks.
My question is whether this is an acceptable convention in the mathematical community. I am not a native speaker of the English language, but as far as my understanding goes the words "so-called" are typically used negatively, to put down the object being referred to. This is the colloquial usage of "so-called" that I am aware of. It is quite possible that conventions differ in technical fields, and even among different technical fields.
So, does the phrase "so-called" have any negative connotations when used in mathematics as in the examples above? And if it does not, is the usage common enough that the chances of being misunderstood when using it are small?
I checked the English Language and Usage SE for a discussion on the use of this phrase and came across this question. It seems the consensus there is that it is context dependent, and it is usually used neutrally in technical writing. But I still felt it would be better to ask here to get a more mathematics-specific viewpoint.