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Let 𝐴 and Ω be sets, and suppose [that with each element 𝛼 of 𝐴 there is associated a subset of Ω which we denote by 𝐸𝛼].

Is "associated a subset of Ω" grammatical in this sentence?

An anonymous person said that the word "there" is inverted with the noun phrase "a subset of Ω." But I think the pronoun "there" is the grammatical subject of the bracketed that-clause, and the noun phrase "an associated subset of Ω which we denote by 𝐸𝛼" should be the semantic subject of the clause. The noun "subset" would be the head of this semantic subject.

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  • Sounds fine to me.
    – mdewey
    Apr 23, 2022 at 13:23
  • In my opinion the sentence sounds grammatically wrong, but I'm not 100% sure
    – DialFrost
    Apr 23, 2022 at 13:25

1 Answer 1

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The structure sounds a little weird, but it makes sense. Here's an example from 1 Corinthians 12:8, New International Version:

To one [person] there is given through the Spirit a message of wisdom.

This can be reorganized in the following way to eliminate existential there:

A message of wisdom is given through the Spirit to one [person].

I also find OP's exact text in a textbook published by McGraw-Hill, which makes it pretty legitimate in my eyes.

I find this similar usage in a very carefully typeset handout used by some math class in Washington University of St. Louis, a reputable school:

to each element of I there is associated a subset Si ⊂ S.

You would have to ask a mathematician to know if the structure is commonly used in the field.

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  • Thank you for your explanation!
    – Bulhwi Cha
    Apr 23, 2022 at 14:25

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