Mathematical writing tend to be very repetitive. To be clear, I do not consider this as something necessarily evil: Mathematics is a language in its own right, and a very technical one, where most of the effort is to be put on the value of the mathematical content.
On the other hand, I do often find myself trying hard (but not necessarily with success!) to make my write-ups in English look smoother from the point of the exposition. In particular, I like avoiding to repeat the very same stylistic elements in consecutive sentences whenever this is possible (that is, I happen to know how to do): For instance, by alternating sentences of the form "[...] there exists an object X such that [...]" to sentences of the form "[...] there is determined an object Y for which [...]". However, someone in my circles made me notice that my use of "there is determined" may not be correct, and this is the reason why I'm back to you again:
Is it legitimate to use "there is determined" in the way I'm doing in the above, as an alternative to "there exists"?
I know I could just use "there is", but my question is about "there is determined", which, in some situations, sounds better to my ears (except that it might be incorrect!).