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Iterates of $M_1$
Assume $\boldsymbol {{\Delta }}^1_{2}$-determinacy. Let $L_{\kappa _3}[T_2]$ be the admissible closure of the Martin-Solovay tree and let $M_{1,\infty }$ be the direct limit of all iterates of $M_1$ via countable trees. We show that $L_{\kappa _3}[T_2] \cap V_{u_{\omega }}$ is the universe of $M_{1,\infty } | u_{\omega }$.