Abstract corrected iterations

We consider \((<\lambda )\) $(<\lambda )$ -support iterations of a version of \((<\lambda )\) $(<\lambda )$ -strategically complete \(\lambda ^+\) ${\lambda }^{+}$ -c.c. definable forcing notions along partial orders. We show that such iterations can be corrected to yield an analog of a result by Judah and Shelah for finite support iterations of Suslin ccc forcing, namely that if \((\mathbb {P}_{\alpha }, \underset{\sim }{{\mathbb {Q}}_{\beta }}: \alpha \le \delta , \beta <\delta )\) $({\mathbb{P}}_{\alpha },\underset{\sim }{{\mathbb{Q}}_{\beta }}:\alpha \le \delta ,\beta <\delta )$ is a FS iteration of Suslin ccc forcing and \(U\subseteq \delta \) $U\subseteq \delta$ is sufficiently closed, then letting \(\mathbb {P}_U\) ${\mathbb{P}}_U$ be the iteration along U, we have \(\mathbb {P}_U \lessdot \mathbb {P}_{\delta }\) ${\mathbb{P}}_U⋖{\mathbb{P}}_{\delta }$ .