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Prikry forcing and tree Prikry forcing of various filters

  • Tom BenhamouEmail author
Article
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Abstract

In this paper, we answer a question asked in Koepke et al. (J Symb Logic 78:85–100, 2013) regarding a Mathias criteria for Tree-Prikry forcing. Also we will investigate Prikry forcing using various filters. For completeness and self inclusion reasons, we will give proofs of many known theorems.

Keywords

Prikry forcing Intermediate models None-normal ultrafilter 

Mathematics Subject Classification

03E40 

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Notes

Acknowledgements

The author would like to thank his supervisor Prof. Moti Gitik and Eilon Bilinsky for their mathematical and non–mathematical support. Also he would like to thank the Referee for his detailed and careful examination of the paper.

References

  1. 1.
    Benhamou, T., Gitik, M.: Sets in magidor generic extensions (preprint) (2016)Google Scholar
  2. 2.
    Bukovsky, L.: Iterated ultrapower and prikry’s forcing. Comment. Math. Univ. Carol. 18, 77–85 (1977)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Cummings, J.: Iterated Forcing and Elementary Embeddings. Chapter in Handbook of Set Theory, pp. 776–847 (2009)Google Scholar
  4. 4.
    Dehornoy, P.: Iterated ultrapower and prikry forcing. Ann. Math. Logic 15, 109–160 (1978)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Devlin, K.J.: Some weak versions of large cardinal axioms. Ann. Math. Logic 5, 291–325 (1973)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Devlin, K.J.: Some remarks on changing cofinality. J. Symb. Logic 39, 27–30 (1974)CrossRefzbMATHGoogle Scholar
  7. 7.
    Dodd, A.J., Jensen, R.B.: The covering lemma for l[u]. Ann. Math. Logic 22, 127–135 (1982)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Gitik, M., Kanovei, V., Koepke, P.: Intermediate models of prikry generic extensions (preprint) (2010)Google Scholar
  9. 9.
    Jech, Thomas: Set Theory Third Millennium Edition. Springer, Berlin (2002)Google Scholar
  10. 10.
    Kanamori, A.: Ultrafilters over a measurable cardinal. Ann. Math. Logic 10, 315–356 (1976)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Ketonen, J.: Ultrafilters over a measurable cardinal. Fundam. Math. 77, 257–269 (1973)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Koepke, P., Rasch, K., Schlicht, P.: Minimal prikry-type forcing for singularizing a measurable cardinal. J. Symb. Logic 78, 85–100 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Kunen, K.: Introduction to Independence Proofs. North-Holand, Amsterdam (1980)zbMATHGoogle Scholar
  14. 14.
    Mathias, A.R.D.: On sequences generic in the sense of prikry. J. Aust. Math. Soc. 15, 409–414 (1973)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Prikry, K.: Changing measurable into accessible cardinals. Diss. Math. 68, 5–52 (1970)MathSciNetzbMATHGoogle Scholar
  16. 16.
    Shelah, S.: Proper and Improper Forcing. Springer, Berlin (1998)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsTel-Aviv UniversityTel-AvivIsrael

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