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

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


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.


  1. 1.
    Kanamori, A.: Higher Infinite: Large Cardinals in Set Theory from Their Beginnings. 2nd Edn. Springer Monographs in Mathematics, Springer, Berlin (2003)Google Scholar
  2. 2.
    Schindler, R.: Set Theory: Exploring Independence and Truth. Springer (2014)Google Scholar
  3. 3.
    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

Personalised recommendations