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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Iterates of $ M_1$


Author: Yizheng Zhu
Journal: Trans. Amer. Math. Soc. 371 (2019), 8811-8827
MSC (2010): Primary 03E15, 03E45, 03E55, 03E60
DOI: https://doi.org/10.1090/tran/7671
Published electronically: February 21, 2019
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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 } \vert u_{\omega }$.


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Yizheng Zhu
Affiliation: Institut für mathematische Logik und Grundlagenforschung, Fachbereich Mathematik und Informatik, Universität Münster, Einsteinstr. 62, 48149 Münster, Germany
Address at time of publication: School of Mathematical Sciences, University of Chinese Academy of Sciences, 19A Yuquan Road, Beijing 100049, People’s Republic of China
Email: zhuyizheng@gmail.com

DOI: https://doi.org/10.1090/tran/7671
Received by editor(s): December 6, 2017
Received by editor(s) in revised form: July 30, 2018
Published electronically: February 21, 2019
Article copyright: © Copyright 2019 American Mathematical Society