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The Boldface Martin-Harrington Theorem in \(\mathsf{Z_2}\)

  • Yong ChengEmail author
Chapter
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Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Abstract

The Boldface Martin-Harrington Theorem is the relativization of the Martin-Harrington Theorem. The former expresses that \(Det(\varvec{\varSigma _1^1})\) if and only if for any real x, \(x^{\sharp }\) exists. In this chapter, I prove the Boldface Martin-Harrington Theorem in \(\mathsf{Z_2}\) . In Sect. 3.1, I prove in \(\mathsf{Z_2}\) that if for any real \(x, x^{\sharp }\) exists, then \(Det(\varvec{\varSigma _1^1})\) holds. In Sect. 3.2, I prove in \(\mathsf{Z_2}\) that \(Det(\varvec{\varSigma _1^1})\) implies that for any real x, \(x^{\sharp }\) exists.

References

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    Schindler, R.: Set Theory: Exploring Independence and Truth. Springer (2014)Google Scholar
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    Jech, T.J.: Set Theory. Third Millennium Edition, revised and expanded. Springer, Berlin (2003)Google Scholar

Copyright information

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.School of PhilosophyWuhan UniversityWuhanChina

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