Archive for Mathematical Logic

, Volume 58, Issue 1–2, pp 71–75 | Cite as

Extendible cardinals and the mantle

  • Toshimichi UsubaEmail author


The mantle is the intersection of all ground models of V. We show that if there exists an extendible cardinal then the mantle is the smallest ground model of V.


Extendible cardinal Mantle Set-theoretic geology 

Mathematics Subject Classification

03E45 03E55 


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of Science and EngineeringWaseda UniversityShinjyukuJapan

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