Iterates of 𝑀₁

Zhu, Yizheng

doi:10.1090/tran/7671

Iterates of $M_1$
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by Yizheng Zhu PDF

Trans. Amer. Math. Soc. 371 (2019), 8811-8827 Request permission

Abstract:

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 $M_{1,\infty } | u_{\omega }$.

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