As in the title, I'm looking for examples of $\Sigma^1_4$ (preferably complete) sentences which are independent from ZFC in both ways, namely given a model $V$ we can extend it to $V'$ were such a sentence holds, but also extend it to a model $V''$ were such sentence fails.

By Shonfield Theorem $\Sigma_4^1$ (or $\Pi^1_4$) is the lowest avaible complexity of such formula, and that's why I'm looking for such examples.

As in the title, I'm looking for examples of $\Sigma^1_4$ (preferably complete) sentences which are independent from ZFC in both ways, namely given a model $V$ we can extend it to $V'$ where such a sentence holds, but also extend it to a model $V''$ where such sentence fails.

By Shoenfield Theorem $\Sigma_4^1$ (or $\Pi^1_4$) is the lowest available complexity of such a formula, and that's why I'm looking for such examples.