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Archive for Mathematical Logic

, Volume 56, Issue 7–8, pp 1037–1044 | Cite as

Codings and strongly inaccessible cardinals

  • Tadatoshi MiyamotoEmail author
Article

Abstract

We show that a coding principle introduced by J. Moore with respect to all ladder systems is equiconsistent with the existence of a strongly inaccessible cardinal. We also show that a coding principle introduced by S. Todorcevic has consistency strength at least of a strongly inaccessible cardinal.

Keywords

Simplified morasses Strongly inaccessible cardinals Bounded Martin’s Maximum BPFA \(\theta _{AC}\) \(v_{AC}\) 

Mathematics Subject Classification

03E50 03E57 03E35 

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References

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    Devlin, K.J.: Constructibility, Perspectives in Mathematical Logic. Springer, Berlin (1984)Google Scholar
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    Miyamoto, T.: A coding and a strongly inaccessible cardinal (a note, 2008)Google Scholar
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    Moore, J.: Set mapping reflection. J. Math. Log. 5(1), 87–97 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
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    Todorcevic, S.: Generic absoluteness and the continuum. Math. Res. Lett. 9, 1–7 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
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    Velleman, D.: Simplified morasses. J. Symb. Log. 49(1), 257–271 (1984)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Nanzan UniversityShowa-ku, NagoyaJapan

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