Do I need to use "is there" or "there is" in the following sentence?
It is natural to ask under which conditions is there a subtype relation between two given arrow types.
If I change "is" to "be" the order is clearly "there be".
Do I need to use "is there" or "there is" in the following sentence?
It is natural to ask under which conditions is there a subtype relation between two given arrow types.
If I change "is" to "be" the order is clearly "there be".
The correct order in the sentence is “there is”.
The inversion of the subject-verb word order mainly occurs in questions. When the interrogative clause is a question on its own, the correct order is “Is there”:
Under which conditions is there a subtype relation between two given arrow types?
When cited as a direct quotation, that inversion order remains:
It is natural to ask: “Under which conditions is there a subtype relation between two given arrow types?”
But when used as a subordinate interrogative clause, the normal subject-verb word order is used:
It is natural to ask under which conditions there is a subtype relation between two given arrow types.
Edit: it’s a subordinate interrogative clause, not a relative clause. Hat tip: BillJ in comment below.
One might ask what conditions are necessary and sufficient that there be a subtype relation between two arrow types.
– Jim Newton Oct 02 '18 at 16:58"Is there" is used in argumentative sentences.
Is there someone over the hill?
"There is" is used in affirmative sentences.
There is a cow over the hill.
So it would be more common to write your phrase like this:
It is natural to ask under which conditions there is a subtype relation between two given arrow types.
The latter is technically correct. The former leans towards colloquial. Both are awkward. Consider changing it to:
It would be logical to ask under which conditions a subtype relation would exist [or: emerge; or: become obvious; or: manifest itself] between two given arrow types.
Or:
It would only be logical to ask under which conditions a subtype relation between two given arrow types would become evident.
Or:
One would be naturally inclined to ask at that point under which conditions a subtype relation between two given arrow types would manifest itself.
It is natural to ask [under which conditions is there / there is a subtype relation between two given arrow types].
The bracketed constituent is a subordinate interrogative clause (embedded question). Unlike main clause interrogatives, there is normally no inversion, so “there is” is the correct version.
The meaning can be glossed as:
"It is natural to ask the answer to the question 'Under which conditions is there a subtype relation between two given arrow types?'"