# Infinity-Borel sets in ZFC

The notion of an $\infty$-Borel set of reals is useful in the study of AD. Under ZFC it becomes trivial: every set of reals is $\infty$-Borel. However, the notion of an $\infty$-Borel code is still interesting. For example, an $\infty$-Borel code $S$ gives us an absolute way to define a set of reals $(A_S)^{V[g]}$ in a generic extension $V[g]$, albeit without some of the nice properties of uB-codes. So I have two related questions:

(1) What are some applications of $\infty$-Borel codes in ZFC?

(2) What are some applications where an $\infty$-Borel code is used to define a set of reals in a generic extension?

I am discounting the special case of $\omega$-Borel codes, that is, ordinary codes for Borel sets.

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