Meaning of "集合论提供了要如何描述数学物件的语言" in an article on set theory

Question

Here is a sentence from the Baidu Baike article on set theory 集合论. I am trying to read this article using a dictionary because it has many words that I have not seen before.

在大多数现代数学的公式化中，集合论提供了要如何描述数学物件的语言。

Zài dàduōshù xiàndài shùxué de gōngshìhuà zhōng, jíhélùn tígōngle yào rúhé miáoshù shùxué wùjiàn de yǔyán.

I am pretty sure that the first part translates to In the formalization of most of modern mathematics, ....

I think that the second part translates to something similar to set theory provides the language for describing mathematical objects. For the second part, I am guessing based on context.

However, I don't know what 要如何 contributes to the meaning. Also, I don't know why 提供 appears with the perfective marker 了. The article might be saying that set theory has provided a language for describing mathematics, and describing a change in modern math from a historical perspective.

How do you actually translate this sentence? What are 了 and 要如何 contributing to its meaning?

Answer 1

集合论(set theory) is the subject.

提供了(provide) is the verb, where '了' marks the action as complete at the time we are talking about.

要如何描述数学物件(how to describe math objects) is an attributive clause that modifies '语言', the object.

This sentence is grammarly problematic though, it feels like google translated, 集合论提供了描述数学物件的语言 would be more natural.